Step-by-step explanation:
prism
v=1/2 X 12cm X 8cm
V= 48
rectangular prism
v=80cm+48cm
v=128cm
Which of the following graphs represent a function? Check all that apply.
A curve that rises from left to right, graphed in a coordinate plane
A graph in a coordinate plane. The graph starts as a line that ascends from left to right. Then it becomes a vertical line going up.
A graph in a coordinate plane. The graph begins at 0, 0 and curves up and down, creating peaks and valleys. As the graph moves to the right, the peaks and valleys get smaller and closer together.
Three-quarters of a circle, graphed in a coordinate plane
A graph in a coordinate plane. The graph curves up and down, creating peaks and valleys, but there is no pattern to these peaks and valleys.
A graph in a coordinate plane. The graph curves back and forth, from left to right.
What is the meaning of "free variables"?
Free variables are variables used to represent parameters
What are free variables?Free variables are placeholders or symbols in mathematics and logic that are not constrained by any quantifiers or other specified conditions within an expression, formula, or equation.
When the expression is evaluated, they stand for values that can change or be given different values. In equations or functions, free variables are frequently employed to represent unknowns or parameters.
Free variables enable flexibility and generality in mathematical reasoning since they can be given various values to investigate various situations or solutions. In contrast, bound variables have a specific scope within a certain context or statement and are constrained by quantifiers.
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A population data set produced the following information N-250 Σx=9880, Σy=1456. Σxy-85080 Σx²=485870, Σy² = 135675 Find the value of oe and p²
The value of p² is approximately 0.999999528.
To find the value of oe (the standard error of estimate) and p² (the coefficient of determination), we can use the given population data set information.
The formula for the standard error of estimate (oe) is:
oe = √((Σy² - (Σy)² / N) / (N - 2))
Substituting the given values, we have:
oe = √((135675 - (1456)² / 250) / (250 - 2))
oe = √((135675 - 2124736 / 250) / 248)
oe = √(541.96)
oe ≈ 23.27
Therefore, the value of oe is approximately 23.27.
The coefficient of determination (p²) can be calculated using the formula:
p² = 1 - (Σxy - (Σx × Σy) / N) / ((Σx² - (Σx)² / N) × (Σy² - (Σy)² / N))
Substituting the given values:
p² = 1 - (85080 - (9880 × 1456) / 250) / ((485870 - (9880)² / 250) × (135675 - (1456)² / 250))
p² = 1 - (85080 - 14358080 / 250) / ((485870 - 968144 / 250) × (135675 - 2124736 / 250))
p² = 1 - (85080 - 57432.32) / (478352.56 × 123346.74)
p² = 1 - (27647.68) / (59022875580.02)
p² ≈ 0.999999528
Therefore, the value of p² is approximately 0.999999528.
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Help me a123 sq ft
B61 sq ft
C49sq ft
D110 sq ft
The area of the required shaded portion is 123 ft²
Given is figure having some shaded portion we need to find the area of the same,
So, the shaded portion is two right isosceles triangles with equal side measuring 14 ft and 7 ft,
So, to find the same, we will calculate the area of the triangles and add them,
Area of a triangle = 1/2 x base x height
Area of the shaded portion = 1/2 x 7 x 7 + 1/2 x 14 x 14
= 122.5 ft²
≈ 123 ft²
Hence the area of the required shaded portion is 123 ft²
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
A. mBC = 71
B. mAB = 142
C. AD = 30
D. BD = 30
E. YD = 16
F. DC = 18
Step-by-step explanation:
A. mBC = mAC = 71
B. mAB = mBC + mAC = 71 + 71 = 142
C. AD = AB/2 = 60/2 = 30
D. BD = AD = 30
E. YA^2 = YD^2 + AD^2
YD^2 = YA^2 - AD^2 = 34^2 - 30^2 = 1156 - 900 = 256
YD = √256 = 16
F. DC + YD = YC
DC = YC - YD = 34 - 16 = 18
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
A. 19.8
B. 15.9
Step-by-step explanation:
A.
To find the geometric mean between two numbers, you multiply them together and then take the square root of the product.
28 × 14 = 392
[tex]\sqrt{392}[/tex] = 19.799 ≈ 19.8
B.
7 x 36 = 252
[tex]\sqrt{252}[/tex] = 15.8745 ≈ 15.9
variable of 10(n+3)=1,000,00
Answer: Distribute the 10 on the left side of the equation:
10n + 30 = 1,000,000
Subtract 30 from both sides of the equation to isolate the term with n:
10n = 1,000,000 - 30
10n = 999,970
Divide both sides of the equation by 10 to solve for n:
n = 999,970 / 10
n = 99,997
Therefore, the value of the variable n that satisfies the equation 10(n + 3) = 1,000,000 is n = 99,997.
Step-by-step explanation:
There is a substance called sodium-24 that decays at a rate of 4.5% per hour, compounded continuously.
You start with a sample of 500 grams of this substance.
a) Write a function to model the amount remaining after t hours.
The function to model the amount remaining after t hours is:
[tex]A(t) = 500 \times e^{-0.045t}[/tex]
We have,
To model the amount remaining after t hours for the substance sodium-24, which decays at a rate of 4.5% per hour compounded continuously, we can use the formula for continuous exponential decay:
[tex]A(t) = A(0) \times e^{-rt}[/tex]
Where:
A(t) is the amount remaining after t hours,
A(0) is the initial amount,
e is the base of the natural logarithm (approximately 2.71828),
r is the decay rate (expressed as a decimal).
In this case,
The initial amount A(0) is 500 grams, and the decay rate r is 4.5% per hour, which can be expressed as 0.045 (decimal form).
Thus,
The function to model the amount remaining after t hours is:
[tex]A(t) = 500 \times e^{-0.045t}[/tex]
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Find the equation of the axis of symmetry of the following parabola algebraically. y=−3x^2−42x−159
The equation of the axis of symmetry is x = -7.
Given is an equation of a parabola, y = -3x² - 42x - 159, we need to find the equation of the axis of the symmetry.
To find the equation of the axis of symmetry of a parabola in the form of y = ax² + bx + c, you can use the formula x = -b / (2a).
In this case, the given equation is y = -3x² - 42x - 159.
Comparing it to the general form, we have a = -3 and b = -42.
Applying the formula, we can calculate the x-coordinate of the vertex (the axis of symmetry):
x = -b / (2a)
x = -(-42) / (2(-3))
x = 42 / (-6)
x = -7
Therefore, the x-coordinate of the vertex is -7.
To find the equation of the axis of symmetry, we use the value of x in the form x = h, where (h, k) is the vertex.
Hence, the equation of the axis of symmetry is x = -7.
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Lucas wants to create a triangle with sides measuring 9 inches 13 inches and 15 inches. He says that more than one triangle is possible given the side lengths. What time about Lucas claim is true?
The Triangle Inequality Theorem holds for these values, and only one triangle is possible with these side lengths. Lucas' claim is false.
What is Triangle Inequality Theorem ?According to the Triangle Inequality Theorem, any two triangle sides' sums must be greater than the length of the third side. In other words, the following three inequalities must hold for any three positive numbers, a, b, and c:
a+b>c
a+c>b
b+c>a
In this case, a=9, b=13, and c=15. Let's check if the Triangle Inequality Theorem holds for these values:
9+13>15 (true)
9+15>13 (true)
13+15>9 (true)
Therefore, the Triangle Inequality Theorem holds for these values, and only one triangle is possible with these side lengths.
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I have 7/4 green counters, and 24 yellow counter, so how much green counters will i have
Answer: the question doesn't give that much information but you would have 7/4 or 1.75 green counters.
Step-by-step explanation: 7/4 as a decimal is 1.75
JOSON Ortiz Budgeting Basics with Autumn Autumn is 22 years old and works as a checker at a local grocery store. Autumn lives in an apartment she shares with two other roommates. Autumn's take-home pay from her job is $1275.00 per month. Add this amount to her bank registry below. Here is a list of how Autumn will be budgeting her money this month. Move the expenses over to the bank registry and deduct them from the balance. Rent - $400.00 Utilities- $75.00 Cell Phone - $80.00 Subway Pass - $120.00 Groceries - $200.00 Work Clothes- $100.00 Entertainment $100.00 Savings $200.00 Transaction Paycheck Withdrawal Deposit Ending Balance Balance
Autumn's bank registry will be :
Transaction Amount Balance
Paycheck $1275.00 $1275.00
Rent $400.00 $875.00
Utilities $75.00 $800.00
Cell Phone $80.00 $720.00
Subway Pass $120.00 $600.00
Groceries $200.00 $400.00
Work Clothes $100.00 $300.00
Entertainment $100.00 $200.00
Savings $200.00 $0.00
How to explain the informationAs you can see, Autumn has $0.00 left over at the end of the month. This means that she is spending more money than she is earning. In order to create a budget that works for her, Autumn will need to find ways to cut back on her expenses. Some possible areas where she could cut back include:
Autumn could look for a cheaper apartment or move in with more roommates. Autumn could turn off lights and appliances when she's not using them and seal up any cracks or holes in her apartment to keep the heat in during the winter and the cool air in during the summer.
By cutting back on her expenses, Autumn can create a budget that works for her and save money for the future.
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amara finds the sum of two number cubes rolled at the same time. The chart below shows all possible sums from the 36 possible combinations when rolling two number cubes. How many times should Tamara expect the sum of the two cubes be equal to if she rolls the two number cubes 180 times?
Tamara should expect the sum of the two cubes to be equal to 7 around 30 times when rolling the two number cubes 180 times.
To determine how many times Tamara should expect the sum of the two number cubes to be equal to a certain value, we need to analyze the chart and calculate the probabilities.
Let's examine the chart and count the number of times each sum occurs:
Sum: 2, Occurrences: 1
Sum: 3, Occurrences: 2
Sum: 4, Occurrences: 3
Sum: 5, Occurrences: 4
Sum: 6, Occurrences: 5
Sum: 7, Occurrences: 6
Sum: 8, Occurrences: 5
Sum: 9, Occurrences: 4
Sum: 10, Occurrences: 3
Sum: 11, Occurrences: 2
Sum: 12, Occurrences: 1
Now, let's calculate the probabilities of each sum occurring.
Since there are 36 possible combinations when rolling two number cubes, the probability of each sum is the number of occurrences divided by 36:
Probability of sum 2 = 1/36
Probability of sum 3 = 2/36
Probability of sum 4 = 3/36
Probability of sum 5 = 4/36
Probability of sum 6 = 5/36
Probability of sum 7 = 6/36
Probability of sum 8 = 5/36
Probability of sum 9 = 4/36
Probability of sum 10 = 3/36
Probability of sum 11 = 2/36
Probability of sum 12 = 1/36
To find out how many times Tamara should expect a certain sum when rolling the two number cubes 180 times, we can multiply the probability of that sum by 180.
For example, to find the expected number of times the sum is 7:
Expected occurrences of sum 7 = (6/36) [tex]\times[/tex] 180 = 30
Similarly, we can calculate the expected occurrences for all other sums.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
ABC forms a right-angled triangle
Let the distance between AB = x
Using Pythagoras theorem
Sin 30 = Opposite / Hypoteneuse
Sin 30 = 12 in/ x
However, From the equilateral triangle, all sides are = 2 and the angles are all = 60 degrees. Then we take a right-angled triangle out of it. This means that the base equals 1, and the top side is halved and equals 30 degrees.
Using Pythagoras' theorem, Sin 30 = 1/ 2
Substituting back into the equation, we get:
1/ 2 = 12 in / x
Cross multiplying, we get:
x = 24 in
Recall x = AB
AB = 24 inches
To remember the angles and their respective formula, use SOHCAHTOA
Where sin x = Opposite / Hypoteneuse
Cos x = Adjacent / Hypoteneuse
Tan x = Opposite / Adjacent
The distribution of scores on a history test is close to normal. The scores are adjusted so that the mean score is about =75
and the standard deviation is =5
. What percent of the scores fall between 65 and 75?
13.5%
27.0%
47.5%
The percentage of scores that fall between 65 and 75 is approximately [tex]2 \times 34 = 68%.[/tex]%
To determine the percentage of scores that fall between 65 and 75, we can use the properties of the normal distribution.
Mean score = 75
Standard deviation = 5
We know that the normal distribution is symmetric around the mean, and approximately 68% of the data falls within one standard deviation from the mean.
This means that about 34% of the scores fall between the mean and one standard deviation above the mean.
To calculate the percentage of scores between 65 and 75, we need to determine how many standard deviations away from the mean 65 and 75 are.
For 65:
(65 - 75) / 5 = -2
For 75:
(75 - 75) / 5 = 0
From the calculations, we can see that 65 is 2 standard deviations below the mean, and 75 is at the mean.
Since the distribution is symmetric, we can consider the percentage of scores between the mean and one standard deviation above the mean (34%) and double it to account for the scores between the mean and one standard deviation below the mean.
Therefore, the percentage of scores that fall between 65 and 75 is approximately 2 [tex]\times[/tex] 34% = 68%.
However, none of the given answer options match the calculated result. Therefore, none of the provided answer options accurately represent the percentage of scores between 65 and 75 based on the given information.
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What is the the measure of
A
B
40°
?
C
Answer:
Step-by-step explanation:
To find the measure of angle A
The line r represents f ( x ) = x − 4 3 . Therefore, the line that represents f - 1 is and f - 1 ( x ) = x + .
Given statement solution is :- The Inverse line that represents [tex]f^(-1[/tex]) is [tex]f^(-1)[/tex] (x) = 3x + 4.
To find the inverse function of f(x) = (x - 4)/3, we need to swap the roles of x and y and solve for y. Let's start by writing the equation with y instead of f(x):
y = (x - 4)/3
Now, let's interchange x and y:
x = (y - 4)/3
To solve for y, we can isolate it by multiplying both sides of the equation by 3:
3x = y - 4
Next, let's add 4 to both sides:
3x + 4 = y
Finally, we can write the inverse function as:
[tex]f^(-1)(x)[/tex] = 3x + 4
So, the Inverse line that represents [tex]f^(-1[/tex]) is [tex]f^(-1)[/tex] (x) = 3x + 4.
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Express log 161 in the form of loga + logb.
log 161 can be expressed as log 7 + log 23 in the form of loga + logb.
To express log 161 in the form of loga + logb, first we need to find suitable values for a and b such that their logarithmic product is equal to log 161.
Let's find the factors of 161 :
161 = 7 * 23
Now, we can express log 161 as product of two logarithms :
log 161 = log (7 + 23)
Using the logarithmic property log(a*b) = log a + log b :
log 161 = log 7 + log 23
Therefore, log 161 can be expressed as log 7 + log 23.
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100 Points! Geometry question. Photo attached. Find the area of the figure. Round to the nearest tenth if necessary. Please show as much work as possible. Thank you!
Answer:
626.71 cm^2
Step-by-step explanation:
Area of figure = area of half circle + Area of half circle + area of a rectangle
here, diameter=15 cm
radius = 15/2=7.5 cm
length=30cm
breadth=15cm
Now
Area of figure = 1/2*π*radius^2+ 1/2*π*radius^2+length*breadth
=1/2* 1/2*π*7.5^2+1/2* 1/2*π*7.5^2+30*15
=626.71 cm^2
An artist makes a hanging sculpture out of rhombus-shaped pieces. Each rhombus shape has diagonals of 3.5 centimeters and 5 centimeters. What is the area of each rhombus? 4.25 cm2 8.5 cm2 8.75 cm2 17.5 cm2
The area of each rhombus is 8.75 [tex]cm^2[/tex]. The correct option is 8.75 [tex]cm^2.[/tex]
To find the area of each rhombus, we can use the formula for the area of a rhombus:
Area = (diagonal1 × diagonal2) / 2
Given that the diagonals of the rhombus-shaped pieces are 3.5 centimeters and 5 centimeters, we can substitute these values into the formula:
Area = (3.5 cm × 5 cm) / 2
Area = 17.5 [tex]cm^2[/tex] / 2
Area = 8.75 [tex]cm^2[/tex]
Therefore, the area of each rhombus is 8.75 [tex]cm^2[/tex]. The correct option is 8.75 [tex]cm^2.[/tex]
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A custom cake baker charges a flat fee for each job, plus an hourly rate for the
number of hours the job takes to complete. The total amount of her bill to the customer can be expressed by 40 + 25h
where h is the hours it takes for the job.what does the coefficient of h, in the expression represent
The coefficient h in the expression means the time taken for the job to be completed in hours.
How to find the value of the coefficient in the expression?The custom cake baker charges a flat fee for each job, plus an hourly rate for the number of hours the job takes to complete. The total amount of her bill to the customer can be expressed by 40 + 25h where h is the hours it takes for the job.
Therefore, the coefficient h in the expression can be interpreted as follows:
total amount of bills = 40 + 25h
where
40 dollars is the flat fee for each job
Then the coefficient h means the hourly rate for the time taken for the job to be completed.
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Arlene has to unpack 4 1/2 boxes of canned pineapple juice. He unpacked 1/4 of them.
How many boxes are still unpacked?
50 Points! Multiple choice geometry question. Photo attached. Thank you!
The area of the slice of pizza is 25.1 inches squared.
How to find the area of the slice of pizza?The circular pizza has a diameter of 16 inches. Each slice of pizza have a angle of 45 degrees.
Therefore, the area of the slice of pizza can be calculated as follows:
area of the slice of pizza = ∅ / 360 × πr²
where
r = radius∅ = central angleTherefore,
r = 16 /2
r = 8 inches
area of the slice of pizza = 45 / 360 × 3.14 × 8²
area of the slice of pizza = 45 / 360 × 3.14 × 64
area of the slice of pizza = 9043.2 / 360
area of the slice of pizza = 25.12 inches²
area of the slice of pizza = 25.1 inches²
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Fill in the y-intercept to complete the function equation.
Answer:
y=3x+5
Step-by-step explanation:
you do 4 times 3 then subtract that from 17
6. A study of seatbelt users and nonusers yielded the randomly selected sample data summarized
in the table. Test the claim that the amount of smoking is independent of seat belt use. Use a
0.05 significance level and a test statistic of 1.358. Find the critical value and state the initial
conclusion.
Wear seat belts
Number of Cigarettes Smoked Per Day
0
1-14
15-34
35 and over
175
Don't wear seat belts 149
20
17
07.815; reject the null hypothesis
09.488; fail to reject the null hypothesis
09.488; reject the null hypothesis
42
41
6
9
(1 point)
Answer:
Step-by-step explanation:
ll hypothesis The critical value for this test is 9.488. Based on the test statistic of 1.358, we fail to reject the null hypothesis that the amount of smoking is independent of seat belt use. In other words, there is not enough evidence to support the claim that seat belt use and smoking habits are related.
Personal Note:
You really need to study, or you will end taking summer courses. trust me school isn't that easy and one time I failed I took summer courses but then I passed these summer courses with god's help. so please focus on your studys.
In this picture b, d, and f are midpoints. Ac=50 ce=60 and bd=35. What is fe
The length of FE is equal to 35 units.
What is the triangle midpoint theorem?In Mathematics and Geometry, the triangle midpoint theorem states that the line segment which connects the midpoints of two (2) sides of a triangle must be parallel to the third side, and it's congruent to one-half of the third side.
By applying the triangle midpoint theorem to the triangle, we have the following:
AE = 1/2(FE)
BD ≅ FE (midpoints of AC and CE)
BD = FE = 35 units.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
The given picture with Midpoints B, D, and F, AC is 50 units, CE is 60 units, and BD is 35 units. The length of segment FE is determined to be 35 units.
In the given picture, let's label the points as A, B, C, D, E, and F. It is mentioned that points B, D, and F are midpoints.
Given information:
AC = 50
CE = 60
BD = 35
Since B, D, and F are midpoints, we know that BD is equal to half of AC and half of CE. Therefore, BD = AC/2 and BD = CE/2.
We are given that BD = 35, so we can set up the equations:
35 = AC/2 ...(Equation 1)
35 = CE/2 ...(Equation 2)
Let's solve Equation 1 for AC:
AC = 35 * 2
AC = 70
Similarly, solving Equation 2 for CE:
CE = 35 * 2
CE = 70
Now, let's consider triangle AFE. Since B and D are midpoints, we know that BD is parallel to FE, and FD is parallel to AE. Therefore, triangle AFE is similar to triangle ADC.
In similar triangles, corresponding sides are proportional. Hence, we can write the following ratios:
FE/AC = FD/AD
Substituting the known values, we get:
FE/70 = 35/AC
Cross-multiplying, we have:
FE * AC = 70 * 35
Since we know AC is 70, we can solve for FE:
FE = (70 * 35) / 70
FE = 35
Therefore, the length of FE is 35 units.
the given information, in the given picture with midpoints B, D, and F, AC is 50 units, CE is 60 units, and BD is 35 units. The length of segment FE is determined to be 35 units.
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From the diagram below, given the side lengths marked, and if we know that < C is congruent to < E, we can say that
If we know that <C is congruent to <E, we can say that: (a). the two triangles are similar by SAS.
How to complete the statementfrom the question, we have the following parameters that can be used in our computation:
The triangles (see attachment)
Two triangles are similar when the ratio of their corresponding sides are equal and their corresponding angles are congruent.
So, we have
Ratio = BC/AC = 6/3 = 2.
Ratio = FE/DE = 4/2 = 2.
Since we know that <C is congruent to <E, we can say that the two triangles are similar by side, angle, side (SAS) criterion.
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Which graph shows the solution set for -4.421.6x-3.6?
←++
-3
←++
-3
-2 -1 0
←+++
-7
-2
-1 0
-7 -6 -5 -4
-6 -5 -4
1
1
-3
♡
2
2
3
-2
3
-2 -1
-1
The graph shows the solution set for -4.4 ≥ 1.6x - 3.6 is Graph I.
To solve the inequality -4.4 ≥ 1.6x - 3.6, we can follow these steps:
Add 3.6 to both sides of the inequality to isolate the term with x:
-4.4 + 3.6 ≥ 1.6x - 3.6 + 3.6
-0.8 ≥ 1.6x
Divide both sides of the inequality by 1.6
-0.8 / 1.6 ≥ 1.6x / 1.6
-0.5 ≥ x
So, the solution to the inequality is x ≤ -0.5.
Now, from the solution the graph for the inequality start with closed dot from 0.5 and move towards the points -0.6, -0.7, -0.8, ....
Thus, the graph shows the solution set for -4.4 ≥ 1.6x - 3.6 is Graph I.
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Need assistance with #8, #9, #10, and #11
Any help will be graetly apprciated. Studying for final exam
Below are the right probabilities for each scenario;
8. P(red, then green) [tex]\frac{1}{32}[/tex]; P(yellow, then blue) = [tex]\frac{1}{16}[/tex] and P(blue both times) [tex]\frac{1}{4}[/tex]
9. The probability of choosing a boy then rolling a number that is at most 4 is [tex]\frac{5}{14}[/tex]
10. The probability that both flights will be delayed is [tex]\frac{2}{7}[/tex].
11. P(nickel, then quarter) [tex]\frac{1}{20}[/tex]; P(penny, then not a dime) [tex]\frac{1}{10}[/tex]; P(both dimes)[tex]\frac{3}{20}[/tex]; P(both nickels) [tex]\frac{1}{20}[/tex]
How do we solve the probability questions?For the compounded probability, we can solve them the following way;
8. a) P(red, then green) = P(red) × P(green) = (2/8) × (1/8) = 1/32
b) P(yellow, then blue) = P(yellow) × P(blue) = (1/8) ×(4/8) = 1/16
c) P(blue both times) = P(blue) × P(blue) = (4/8) ×(4/8) = 1/4
9. There are 28 total students and 6 total outcomes on a standard die.
P(boy, then a number at most 4) = (15/28) × (4/6) = 5/14
10. The probability of the first flight being delayed is 6/14, and the probability of the second flight being delayed is 8/12.
P(both flights delayed) = 6/14 × 8/12 = 2/7
11. There are 25 total coins: 4 pennies, 6 nickels, 10 dimes, and 5 quarters.
a) P(nickel, then quarter) = (6/25) × (5/24) = 1/20
b) P(penny, then not a dime) = (4/25) × (15/24) = 1/10
c) P(both dimes) = (10/25) × (9/24) = 3/20
d) P(both nickels) = (6/25) × (5/24) = 1/20
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Does anyone know how to solve this?