The οppοsite angles οf a parallelοgram are equal.
What is Area οf Parallelοgram?The regiοn in a twο-dimensiοnal plane that a parallelοgram οccupies is knοwn as its area. A parallelοgram is a fοrm with fοur sides with twο geοmetry dimensiοns.
Because the οppοsing sides are equal and parallel, sο it is a unique quadrilateral example. The space bοunded by the fοur sides οf a parallelοgram is knοwn as its area. A parallelοgram's area is calculated as the sum οf its length and height.
The οppοsite sides οf a parallelοgram are parallel. Here, PQ ‖ RT and PR ‖ QT.
The οppοsite sides οf a parallelοgram are equal. Here, PQ = RT and PR = QT
The οppοsite angles οf a parallelοgram are equal. Here, ∠P = ∠T and ∠Q = ∠R
Hence, The οppοsite angles οf a parallelοgram are equal.
Learn more about the Area of Parallelogram, by the following link.
https://brainly.com/question/24291122
#SPJ1
It takes an older pump 5 times as long to drain a certain pool as it does a newer pump. Working together, it takes the two pumps 3 hours to drain the
long will it take the newer pump to drain the pool working alone?
Do not do any rounding.
It would take the newer pump 36 minutes to drain the pool working alone.
To solve this problemLet's call the time it takes the newer pump to drain the pool "t". Then, we know that the older pump takes 5t to drain the pool.
If they work together, their combined rate is the sum of their individual rates. Let's call the rate of the newer pump "r" (in units of pool drained per hour). Then, the rate of the older pump is 1/5 of that, or r/5. Together, their rate is:
r + (r/5) = (6/3) = 2
We can simplify this equation by multiplying both sides by 5:
5r + r = 10
Simplifying, we get:
6r = 10
Dividing both sides by 6, we get:
r = 10/6 = 5/3
So the rate of the newer pump is 5/3 of the pool drained per hour.
To find the time it takes the newer pump to drain the pool, we can use the formula:
rate = work / time
Where "work" is the amount of pool drained (which we can assume is 1, since we're talking about draining the entire pool).
So we can write:
5/3 = 1 / t
Multiplying both sides by t, we get:
5t / 3 = 1
Multiplying both sides by 3/5, we get:
t = 3/5 hours, or 36 minutes
Therefore, it would take the newer pump 36 minutes to drain the pool working alone.
Learn more about simplify here : brainly.com/question/738531
#SPJ1
Vince is twice is sister's age who is 8 years old their mother's age is twice the sum of their ages. How old is their mother?
Vince is 16 years old, his sister is 8 years old, and their mother is 48 years old, where Vince is twice his sister's age and their mother is twice the sum of their ages.
Let's start by assigning variables to the unknown ages. Let V be Vince's age, S be his sister's age, and M be their mother's age. Then we can set up three equations based on the given information:
V = 2S (Vince is twice his sister's age)
S = 8 (His sister is 8 years old)
M = 2(V + S) (Their mother's age is twice the sum of their ages)
Using equation 1 and substituting S = 8, we can solve for Vince's age:
V = 2S
V = 2(8)
V = 16
So Vince is 16 years old.
Using equation 3 and substituting V = 16 and S = 8, we can solve for their mother's age:
M = 2(V + S)
M = 2(16 + 8)
M = 2(24)
M = 48
So their mother is 48 years old.
Therefore, Vince is 16 years old, his sister is 8 years old, and their mother is 48 years old.
To summarize:
Vince is twice his sister's age, and his sister is 8 years old.
Using this information, we can calculate that Vince is 16 years old.
Their mother's age is twice the sum of their ages, so using Vince and his sister's ages, we can calculate that their mother is 48 years old.
Therefore, Vince is 16 years old, his sister is 8 years old, and their mother is 48 years old.
Learn more about equation here:
https://brainly.com/question/10413253
#SPJ4
Are these numbers equivalent? 1/3(r^3) and (r^3)/3
1/3(r³) and (r³)/3 are equivalent expressions because division is commutative and both expressions result in dividing r³ by 3.
What is expression ?
In mathematics, an expression is a combination of one or more numbers, variables, and operators that can be evaluated to produce a value.
Yes, 1/3(r³) and (r³)/3 are equivalent expressions.
This is because division is commutative, meaning that it doesn't matter in which order we divide the numbers. So, we can write (r³)/3 as (1/3)(r³), which is equivalent to 1/3(r³).
In both cases, we are dividing r³ by 3, and the result is the same. Therefore, 1/3(r³) and (r³)/3 are equivalent expressions.
1/3(r³) and (r³)/3 are equivalent expressions because division is commutative and both expressions result in dividing r³ by 3.
To know more about expression visit :
https://brainly.com/question/1859113
#SPJ1
which graph type is best suited for graphing the proportion of green eyes to brown-eyed or blue-eyed students in the class?
A pie chart or a bar graph is best suited for graphing the proportion of green eyes to brown-eyed or blue-eyed students in the class.
What is pie chart?A pie chart is a circular graph that displays data as a set of slices, each representing a proportion of the whole.
A pie chart would show the percentage or fraction of each eye color in relation to the whole, while a bar graph would compare the number of students with each eye color side by side.
Both types of graphs are useful for displaying proportions and comparing different categories.
To know more about bar graph visit:
https://brainly.com/question/13298277
#SPJ1
pleaseeeeeeeeeeeeeeeeeeeeeeee help
Answer:
1/5
Step-by-step explanation:
Which probabilities do you need in order to
calculate P(getting A on 2 or fewer spins)?
-P(0 successes)
-P(1 success)
-P(2 successes)
-P(3 successes)
-P(4 successes)
-P(5 successes)
Answer: A,B, C
part B:
P(getting A on 2 or fewer spins)= Answer: 0. 79
Probability of getting A on 2 or fewer spins is 0.79 using sum of probabilities we individually find.
We must add the odds of receiving A on 0 spins, 1 spin, and 2 spins in order to determine the likelihood of getting A in 2 spins or less.
Probability of not receiving A on the first spin is equal to 0.6 P (getting A on 0 spins) (getting A on 1 spin) Probability of receiving A on the first spin and not receiving A on the second spin, or of receiving A on the second spin and not receiving A on the first spin, is equal to 0.40.6 + 0.60.4 = 0.48.
P(getting A on 2 spins) is the likelihood that A will appear on both the first and second spins, or that A will appear on the second spin even if A did not appear on the first spin, and vice versa. = 0.40.4 + 0.60.40.42 = 0.108
P (receiving A on two or fewer spins) is therefore equal to P (getting A on zero spins), P (getting A on one spin), and P (getting A on two spins). These values are 0.6, 0.48, and 0.108, which add up to 0.788, or roughly 0.79.
Therefore 0.79 is the solution to part B.
Learn more about probabilities here:
https://brainly.com/question/29251028
#SPJ1
Find the surface area of the prism.
5m
4 m
m²
6 m
5m
7 m
Answer:
160m².
Step-by-step explanation:
In this case, the prism has two identical rectangular faces with dimensions of 5m by 4m, and four identical rectangular faces with dimensions of 5m by 6m.
Therefore, the surface area of the prism can be calculated as follows:
Surface Area = 2(5m x 4m) + 4(5m x 6m)
Surface Area = 40m² + 120m²
Surface Area = 160m²
So the surface area of the prism is 160m².
What is the phase shift of a periodic function?
a horizontal translation of the function
the horizontal length of one cycle of the function
the number of cycles of the function that occur in one horizontal unit
a vertical translation of the function
A function assigns values. The phase shift of a periodic function is the horizontal translation of the function.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The Phase Shift of a periodic function is the horizontal shift of the function from its normal position. The shift is either left or right.
For example, if the value of c in the function of sine is negative then the function will move towards the right side by the value of c, while if the value of c is positive then the function will towards the left.
Thus, the phase shift of a periodic function is the horizontal translation of the function.
Learn more about Function:
https://brainly.com/question/5245372
The slope of the line that represents the data nicholas collected is -63, and the y- intercept is 825. explain what these represent in the context of the situation. remember that x is the number if days, and y is the number of canned goods
The slope of the line is -63, which represents the number of canned goods decreases at a rate of 63 per day.
The y-intercept is 825, which is the initial amount of canned goods.
What is the slope-intercept form?In Mathematics, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the gradient, slope, or rate of change.x and y represent the data points.c represents the y-intercept or initial value.Based on the information, an equation that models the situation is given by this mathematical expression;
y = mx + c
y = -63x + 825
In conclusion, we can reasonably infer and logically deduce that the slope is -63 and the y-intercept is equal to 825.
Read more on slope here: https://brainly.com/question/12031541
#SPJ1
Write the number in the log as a power of the base, then find y in each equation
y=log3 243
y = loga 1
y = log2 1/64
The number in the log as a power of the base y = -6.
What is logarithmic identity ?
Logarithmic identities are mathematical formulas or rules that are used to manipulate logarithmic expressions. These identities are derived from the properties of logarithms and can be used to simplify or solve logarithmic equations.
The following are some commonly used logarithmic identities:
Product rule: log_a (x * y) = log_a (x) + log_a (y)
This identity states that the logarithm of the product of two numbers is equal to the sum of the logarithms of the individual numbers.
Quotient rule: log_a (x / y) = log_a (x) - log_a (y)
This identity states that the logarithm of the quotient of two numbers is equal to the difference of the logarithms of the individual numbers.
According to the question:
To write the number in the log as a power of the base, we can use the following logarithmic identity:
log_a (x) = y is equivalent to[tex]a^y = x[/tex]
Using this identity, we can rewrite the logarithmic expressions as follows:
y = log3 243 can be written as [tex]3^y = 243[/tex]
y = log2 1/64 can be written as [tex]2^y = 1/64[/tex]
Now, we can solve for y by taking the appropriate power of both sides of each equation:
For the first equation, we can write:
[tex]3^y = 243[/tex]
[tex]3^y = 3^5 (since 243 = 3^5)[/tex]
Therefore, y = 5.
For the second equation, we can write:
[tex]a^y = 1[/tex]
Since any non-zero number raised to the power of 0 is equal to 1, we have:
[tex]a^y = a^0[/tex]
Therefore, y = 0.
For the third equation, we can write:
[tex]2^y = 1/64[/tex]
[tex]2^y = 2^-6 (since 1/64 = 2^-6)[/tex]
Therefore, y = -6.
To know more about logarithmic identity visit:
https://brainly.com/question/30354687
#SPJ1
When you divide a whole number by a fraction how does the quotient compared to the dividend explain
When you divide a whole number by a fraction, the quotient is larger than the dividend.
This is because dividing a whole number by a fraction is the same as multiplying the whole number by the reciprocal (inverse) of the fraction.
For example, if we divide 6 by 1/2, it is equivalent to multiplying 6 by 2, which gives us a quotient of 12. So, the quotient of 12 is larger than the dividend of 6.
This happens because dividing by a fraction means we are dividing the whole into smaller parts, and the more parts we divide it into (i.e., the smaller the fraction), the more of those parts we get. Therefore, the quotient is larger than the dividend as we are getting more of the smaller parts.
To learn more about quotient refer to:
brainly.com/question/16134410
#SPJ4
Suppose a researcher is testing the hypothesis : p versus : p and she finds the P-value to be . Explain what this means. Would she reject the null hypothesis? Why?
Choose the correct explanation below.
A.
If the P-value for a particular test statistic is , she expects results no more extreme than the test statistic in exactly of 100 samples if the null hypothesis is true.
B.
If the P-value for a particular test statistic is , she expects results at least as extreme as the test statistic in about of 100 samples if the null hypothesis is true.
C.
If the P-value for a particular test statistic is , she expects results at least as extreme as the test statistic in exactly of 100 samples if the null hypothesis is true.
D.
If the P-value for a particular test statistic is , she expects results no more extreme than the test statistic in about of 100 samples if the null hypothesis is true.
Part 2
Choose the correct conclusion below.
A.
Since this event is unusual, she will reject the null hypothesis.
B.
Since this event is not unusual, she will not reject the null hypothesis.
C.
Since this event is unusual, she will not reject the null hypothesis.
D.
Since this event is not unusual, she will reject the null hypothesis.
We don't know if she will reject the null hypothesis without knowing the level of significance. But if the p-value is smaller than the level of significance, she would reject the null hypothesis
Why would the researcher reject the null hypothesisThe correct explanation for the P-value is option B: "If the P-value for a particular test statistic is , she expects results at least as extreme as the test statistic in about of 100 samples if the null hypothesis is true."
This means that if the null hypothesis is true, there is a certain probability (represented by the P-value) that we would observe a test statistic as extreme or more extreme than the one we observed in our sample.
As for the conclusion, we cannot determine whether or not the researcher would reject the null hypothesis based solely on the P-value. The decision to reject or not reject the null hypothesis depends on the level of significance (alpha) chosen by the researcher. If the P-value is smaller than the chosen alpha, then the researcher would reject the null hypothesis.
Otherwise, she would fail to reject it. Without knowing the level of significance chosen, we cannot determine the conclusion.
Learn more on null hypothesis here;
https://brainly.com/question/15980493
https://brainly.com/question/25263462
#SPJ1
4
A sports analyst is interested in the relationship
between the number of three-point shots players
attempt in a game and the number of points scored
To investigate the relationship, he collects a simple
random sample of 15 games and records the number
of three-point shots attempted and the total number of
points scored. He finds the equation of the least-
squares regression line to be ý=65.7 +0.729x,
where y is points scored and x is the number of three-
point shots attempted. The residual plot is shown.
Residual
20
10
2
3
Based on the residual plot, is the linear model
appropriate?
7
O No, the residuals are relatively large.
O No, there is a clear pattern in the residual plot
OYes, there is no clear pattern in the residual plot
Yes, about half of the residuals are positive and
half are negative.
Save and Exit
Next
Submit
Answer:
B. No, there is a clear pattern in the residual plot.
Step-by-step explanation:
The residual plot shows the differences between the observed values and the predicted values from the linear regression model. In a good model, the residuals should be randomly scattered around the horizontal line at 0, indicating that the model is capturing all the relevant information in the data.
However, in this case, we can see a clear pattern in the residual plot where the residuals are not randomly scattered around 0. Instead, there seems to be a curved pattern, where the residuals are relatively large for small and large values of x, and relatively small for intermediate values of x. This suggests that the linear model may not be the best fit for the data, and that some other type of model, such as a quadratic or cubic model, may be more appropriate. Therefore, the correct answer is B. No, there is a clear pattern in the residual plot.
Hope this helps! Sorry if it's wrong. If you need more help, ask me! :]
Robert recorded the number of minutes he studied each week for 7 weeks. His data are shown 215,219,165,220,310,238,250
Robert kept track of his study time over the course of seven weeks, and we've mean is [tex]226.43[/tex] minutes, the median is [tex]220[/tex] minutes, the range is [tex]145[/tex]minutes, as well as the standard deviation was [tex]41.98[/tex] minutes.
What can you infer from standard deviation?The extent of data deviation is measured either by standard error. It measures how distant each data point is from the mean. Around 95% of values in any distribution will be within two of the mean's standard deviation.
How may standard deviation be used?First, determine the mean. Step 2: Determine the square of the variation from the mean of each piece of data. Add the values of Step 2 in Step 3. Divide by the total amount of information collected in step 4.
Mean (average):
[tex]Mean = (215 + 219 + 165 + 220 + 310 + 238 + 250) / 7 = 226.43[/tex]
So the average amount of time Robert studied per week is approximately [tex]226.43[/tex] minutes.
Median:
[tex]165, 215, 219, 220, 238, 250, 310[/tex]
The median is the middle value, which is [tex]220[/tex].
Mode:
In this case, there is [tex]0[/tex] value that appears more than once, so there is no mode.
Range:
Range [tex]=[/tex] largest value [tex]-[/tex]smallest value[tex]= 310 - 165 = 145[/tex]
So the range of Robert's study time data is [tex]145[/tex] minutes.
Standard deviation:
Using a calculator or spreadsheet program, we can find the standard deviation to be approximately [tex]41.98[/tex] minutes.
To know more about standard deviation visit:
https://brainly.com/question/23907081
#SPJ1
The lateral surface area of a hollow cylinder is 4224 sq. Cm. It is cut along its height and formed a rectangular sheet of width 33 cm. Find the perimeter of the rectangular sheet
The perimeter of the rectangular sheet is approximately 42.010 cm.
Let's assume the height of the hollow cylinder to be "h", the inner radius to be "r1", and the outer radius to be "r2".
The lateral surface area of the hollow cylinder is given by:
Lateral surface area = 2πrh
We are given that the lateral surface area is 4224 sq. cm, so we can write:
4224 = 2πrh
We also know that the width of the rectangular sheet is 33 cm, which is the same as the circumference of the hollow cylinder. Therefore, we can write:
2πr2 = 33
Solving for r2, we get:
r2 = 33/(2π)
Now, we can use the Pythagorean theorem to find the height of the hollow cylinder:
h^2 = r2^2 - r1^2
We don't know r1, but we can express it in terms of r2 using the fact that the thickness of the hollow cylinder is constant:
r2 - r1 = 33/2π
r1 = r2 - 33/2π
Substituting this expression for r1 in the equation for h, we get:
h^2 = r2^2 - (r2 - 33/2π)^2
Simplifying, we get:
h^2 = 1089/(4π^2)
h = 33/(2π)
Now that we know the values of h and r2, we can find the perimeter of the rectangular sheet:
Perimeter = 2h + 2r2
Perimeter = 2(33/(2π)) + 2(33/(2π))
Perimeter = 66/π + 66/π
Perimeter = 132/π
Using a calculator, we can approximate this value to three decimal places:
Perimeter ≈ 42.010 centimeter
Learn more about lateral surface area here
brainly.com/question/30620880
#SPJ4
If the triangles shown at the right are similar,
what is the value of x?
a - 5in
b - 16.8in
c - 20.4in
d - 30.8
Answer:
b - 16.8in
Step-by-step explanation:
10/x=√34/√96
10/x=5.831/9.798
5.831x=97.98
x=16.803
I NEED HELP ON THIS QUICKLYY WILL GIVE BRAINLIESTTT PLEASE HELP!!!
Answer:
(1)
Let x represent the number of HD Big View TV models produced
let y represent the number of MegaTeleBox models produced
(2)
2x + 3y ≤ 192 manpower constraint
x + y = 72 production capacity constraint
x ≥ 0 Non-negativity constraint
y ≥ 0 Non-negativity constraint
(3)
See attached graph
Step-by-step explanation:
(1)
Let x represent the number of HD Big View TV models produced
let y represent the number of MegaTeleBox models produced
(2)
Constraints
There are a total of 192 person hours per day to manufacture both models so this is the upper limit on the person-hours resource
Each unit of HD Big View takes 2 person-hours so x units will require 2x person-hours
Each unit of MegaTeleBox takes 3 person-hours so y units will require 3y person-hours
Total person-hours to produce x and y units
= 2x + 3y
and this cannot exceed 192.
Therefore the first inequality is manpower resource constraint:
2x + 3y ≤ 192 [1]
Total manufacturing capacity is 72 units. The actual total production is
x + y and this cannot exceed 72
Second inequality is
x + y = 72 [2]
In addition the number of units produced cannot be less than zero. These are the non-negativity constraints:
x ≥ 0, y ≥ 0 [3]
Plugging in all these constraints we get the following system of inequalities
2x + 3y ≤ 192 [1] manpower constraint
x + y = 72 [2] production capacity constraint
x ≥ 0 Non-negativity constraint
y ≥ 0 Non-negativity constraint
(3) See attached graph for this part of the question
The dark shaded region shows the solution set
To show that the company cannot make a negative number of television sets we only consider values on the positive x and y axes
Joey bought 1/2 pound of chocolate to share with his friends. They ate 3/8 pound of the chocolate. How much chocolate does Joey have left?
The amount of chocolate that Joey will have left is; 5/16
How to solve fraction word problems?In word problems on fraction, we will solve different types of problems on multiplication of fractional numbers and division of fractional numbers.
We are given:
Amount of chocolate bought = 1/2 pound of chocolate
Amount of chocolate eaten = 3/8 * 1/2 = 3/16
Thus, the amount of chocolate Joey will have left will be gotten by subtracting the amount eaten from the total amount he bought. Thus;
Amount of chocolate he has left = 1/2 - 3/16
= (8 - 3)/16
= 5/16
Read more about Fraction word problems at; https://brainly.com/question/11562149
#SPJ1
At a 1500 m race, ken ran at an average speed of 200 m/min. How long did it take for ken to finish the race?
Ken took 7.5 minutes to finish the race. We used simple Speed, Distance and Time formula.
The total distance traveled by the object over a given time period is the average speed. A scalar number is the average speed. It does not have a direction and is only represented by the magnitude.
To calculate the time taken by Ken to finish the race, we can use the formula:
Time = Distance/SpeedHere, the distance is 1500m and the average speed of Ken is 200m/min.
So,
Time = 1500/200 = 7.5 minutesTherefore, Ken took 7.5 minutes to finish the race.
Learn more about Speed:
https://brainly.com/question/26046491
#SPJ4
work out the maxuim and minuim amount of hickers that could of walked between 8 and 19 miles help
The maximum and minimum amount of hickers that could of walked between 8 and 19 miles is 19 and 7.
What is minimum and maximum value?The minimum and maximum value depend on the context in which they are being used.
In mathematics, the minimum value refers to the smallest value in a set of numbers or a function, while the maximum value refers to the largest value in the same set of numbers or function. For example, in the set of numbers {2, 4, 5, 7}, the minimum value is 2 and the maximum value is 7.According to question:In general, the minimum and maximum values are the limits or boundaries within which a particular quantity or variable can vary.The minimum number of hikers who could have walked between 8 miles and 19 miles is 7 as it lies in the common interval of 10 ≤ x ≤ 15.The maximum number of hikers who could have walked between 8 miles and 17 miles is 19.To know more about minimum and maximum value visit:
https://brainly.com/question/23504923
#SPJ9
En la figura adjunta, ABC es un cuadrado, AC es diagonal y mide 10 cm. ¿ Cual es el perímetro del cuadrado. A) 20 cm. B) 40 cm. C) (10+10 raíz cuadrada seria 2) cm. D) (5+10 raíz cuadrada seria 2) cm. E) (10+5 raíz cuadrada seria 2) cm
Option E would be (10+5 square root would be 2) cm, which is also incorrect as it does not represent the correct perimeter of the square.
In the figure attached, ABC is a square, AC is diagonal and measures 10 cm. What is the perimeter of the square? A) 20 cm. B) 40 cm. C) (10+10 square root would be 2) cm. D) (5+10 square root would be 2) cm. E) (10+5 square root would be 2) cm.The perimeter of a square is equal to the sum of all four sides. Since ABC is a square, the sides are equal in length. Since AC is the diagonal of the square, it is equal to the length of the two consecutive sides. Therefore, the length of each side AB and BC is equal to 10 cm. Therefore, the perimeter of the square ABC is 20 cm (10 cm x 2). This is option A, 20 cm. The other options are not correct as they do not represent the correct perimeter of the square. Option C would be (10+10 square root would be 2) cm, which is incorrect as it does not represent the correct perimeter of the square. Option D would be (5+10 square root would be 2) cm, which is also incorrect as it does not represent the correct perimeter of the square. Lastly, Option E would be (10+5 square root would be 2) cm, which is also incorrect as it does not represent the correct perimeter of the square.
Learn more about diagonal here:
https://brainly.com/question/30680854
#SPJ4
FIND THE ERROR Armando and Niran want to draw a trapezoid that has a height of 4 units and an area of 18 square units. Armando says that only one trapezoid will meet the criteria. Niran disagrees and thinks that she can draw several different trapezoids with a height of 4 units and an area of 18 square units. Who is correct? Explain your reasoning.
Answer:
Niran is correct.
Step-by-step explanation:
The area of a trapezoid is h(a + b)/2 where h is the height and a and b are the lengths of the opposite parallel sides.
Using the given values:
Area = 18 = 4(a + b)/2
---> 2(a + b) = 18
---> a + b = 9
Now there are many values we can assign to a and b so that they sum to 9 ( for exampl 3 and 6, 4 and 5, 1 and 8)
so Niran is correct.
Carly bought 2 1/4 pounds of apples. she used 2/3 of the apples to make applesauce. how may pounds of apples did she have left
The pounds of apples that she has left is 3/4 pounds.
How many pounds of apples does she have left?A mixed number is a number that is made up of a whole number and a proper fraction. An example of a mixed number is 1 1/4. Where 1 is the whole number and 1 /4 is the proper fraction.
The fraction of the apples used in making the applesauce = 2 1/4 x 2/3
9/4 = 3/2 = 1 1/2
Fraction of apples left = 2 1/4 - 1 1/2
[tex]2\frac{1}{4} - 1\frac{1}{2}[/tex]
[tex]1\frac{1 - 2}{4}[/tex] = [tex]\frac{3}{4}[/tex]
To learn more about multiplication of fractions, please check: https://brainly.com/question/1114498
#SPJ1
Assignment #1 (22PS) 1.9 Practice - Age Problems 1.
A boy is 10 years older than his brother. In 4 years he will be twice as old an his brother. Find the present age of each. 2. A father is 4 times as old as his son. In 20 years the father will be twice as as his son. Find the present age of each.
Hence, in answering the stated question, we may say that As a result, the equation son's current age is x = 10, while the father's current age is 4x = 40.
What is equation?A math equation is a process that relates two statements by using the equals sign (=) to indicate equivalence. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula can be used to understand the link between the two sentences written on opposite sides of a letter. Frequently, the logo and the software are the same. For example, 2x - 4 = 2.
[tex]x + 14 = 2(x + 4)\\x + 14 = 2x + 8\sx = 6[/tex]
As a result, the brother's current age is x = 6, while the boy's current age is x + 10 = 16.
If x is the age of the son, then the father's age is 4x. In 20 years, the son will be x + 20 years old, while the father will be 4x + 20 years old. Because the father will be double his son's age in 20 years:
[tex]4x + 20 = 2(x + 20)[/tex]
Expansion and simplification:
[tex]4x + 20 = 2x + 40\\2x = 20\sx = 10[/tex]
As a result, the son's current age is x = 10, while the father's current age is 4x = 40.
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
can yall help me again i still don't understand this
Answer:
52.
Step-by-step explanation:
So 143 members represent 100% of the population of the problem. A ratio of 4:7 similarly represent 100%. First, you need to get the value of 4:7 in a representation of 100%. You can do that by adding the two (4+7=11) and then dividing it by each value of it. So 7 divided by 11 is .6363, or 63.63% of the whole. Then 4 divided by 11 is .3636, or 36.36% of the whole. After getting this, seeing that the ratio for union members to non union members is 4 union members to 7 nonunion members, and there are 143 employees in total, just get the value of 36.36% of 143; in this case, it's 51.99 - rounded off to 52 employees.
Answer:
52 members
Step-by-step explanation:
Proportional setup.
(4/11)=(x/143)
PLEASE SHOW WORK!!!!!!!!!
For the two functions given, the value for f(g(8)) is option D - 24.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The first function is given as f(x) = x² + 2x.
The second function is given as g(x) = √(2x).
To find f(g(8)), we need to first evaluate g(8) and then plug the result into f(x).
Using g(x) = √(2x), we can find g(8).
Substitute the value of x in the equation -
g(8) = √(2(8))
g(8) = √16
g(8) = 4
Now that we know g(8) = 4, we can find f(g(8)) by plugging in 4 for x in f(x) .
Substitute the value of g(8) in the equation -
f(g(8)) = f(4)
f(g(8)) = 4² + 2(4)
f(g(8)) = 16 + 8
f(g(8)) = 24
Therefore, the solution is obtained as 24.
To learn more about function from the given link
https://brainly.com/question/2284360
#SPJ1
Find WX. PLEASEE HELP
The measurement of WX in the given figure is 22.
What is the median?When a set οf numbers is sοrted in size οrder, the median is the middle value. It is used tο define a set οf data by identifying the numerical midpοint and is a measure οf central tendency. When a grοup οf numbers is οrganized frοm smallest tο largest, the middle number is the οne that shοws up.
A trapezοid's median is the line that divides it intο twο equal sectiοns. The middle line οr the midline is anοther name fοr it. Its length is equal tο the average οf the twο bases οf the trapezοid and runs parallel tο thοse bases.
In the given trapezοid STUV, the length οf the bases ST and UV can be calculated by dividing the median in twο parts and fοlding it and jοining tο tο make a lοng rectangle.
Now the new rectangle is WW'SU where the median was 2wx
In a rectangle opposite side are equal, Therefore
W'W = US
W'W = 2WX
US = UV + ST
= 16 +28
= 44
2WX = 44
WX = 44/2
WX = 22
Thus, The measurement of WX in the given figure is 22.
to learn more about the median visits:
brainly.com/question/26151333
#SPJ1
Here is an expression: 3. 2
1. Evaluate the expression when t is 1,
2. Evaluate the expression when t is 4.
The answer to the equation will be 5, and in the second one the answer to the equation when the value of t is 4 resulted as 14We can evaluate the expression "2 + 3t" for the given values of t:
a. When we consider T as 1 then the substitution can be = 1 as the expression
2 + 3t = 2 + 3(1) = 2 + 3 = 5
Therefore, the value of the expression when t is 1 is 5. to the expression of 2+3t.
b. We substitute t = 4 in the expression and get:
2 + 3t = 2 + 3(4) = 2 + 12 = 14
Therefore, the value of the expression when t is 4 is 14. The value can be 14 when its value is 4.
In the first scenario, the answer to the equation will be 5, and in the second one the answer to the equation when the value of t is 4 resulted as 14. if we give any other number the value changes accordingly.
To know more about expression
brainly.com/question/14083225
The correct question of the answer is
Here is an expression: 2 + 3t
a. Evaluate the expression when t is 1.
b. Evaluate the expression when t is 4.
#SPJ4
i have the slope i just need the length and what it can best be described as please
Answer:
Step-by-step explanation:
all the lengths are the same:
ST = √(-1-2)²+(2-7)² = √9+25 = √34 = 5.831
TU = √(4--1)²+(-1-2)² = √25+9 = √34 = 5.831
UV = √(7-4)²+(4--1)² = √9+25 = √34 = 5.831
VS = √(2-7)²+(4-7)² = √25+9 = √34 = 5.831
The shape is a square (rectangle with equal sides) parallelogram (you could also call it a rhombus)
Use a Double- or Half-Angle Formula to solve the equation in the interval[0,2π). (Enter your answers as a comma-separated list.)cos(θ)−sin(θ)=2sin(2θ)θ=
The solutions of the equation in the interval `[0, 2π)` are `π/3` and `3π/4`.Hence, the required answer is `(π/3, 3π/4)` in comma-separated form.
Given that `cos(θ) - sin(θ) = (2/1) sin(2θ)`, find `θ`.Solution:As we have been given `cos(θ) - sin(θ) = (2/1) sin(2θ)`, we know that we can apply double angle formulae to convert `2θ` to `θ`.`sin(2θ) = 2sin(θ)cos(θ)`∴ `cos(θ) - sin(θ) = (2/1) sin(θ)cos(θ)`⇒ `2 sin(θ) cos(θ) - sin(θ) + cos(θ) = 0`⇒ `sin(θ) (2 cos(θ) - 1) - cos(θ) (2 cos(θ) - 1) = 0`⇒ `(sin(θ) - cos(θ)) (2 cos(θ) - 1) = 0`Therefore, `sin(θ) - cos(θ) = 0` or `cos(θ) = 1/2`Solving `sin(θ) - cos(θ) = 0` gives `θ = 3π/4` (Since `sin(3π/4) = 1/√2` and `cos(3π/4) = -1/√2`)Solving `cos(θ) = 1/2` gives `θ = π/3` (Since `cos(π/3) = 1/2`)Therefore, the solutions of the equation in the interval `[0, 2π)` are `π/3` and `3π/4`.Hence, the required answer is `(π/3, 3π/4)` in comma-separated form.
Learn more about Equation in the interval
brainly.com/question/13551568
#SPJ11