The number of boys and girls that are in this class is equal to 28 students and 14 students respectively.
How to determine the number of boys?In order to determine the number of boys that are in this class with a total population of 42 students, we would have to multiply the total number of students by the fraction representing only the number of boys as follows:
Number of boys, B = 4/6 × Total number of students
Substituting the given parameters into the formula, we have;
Number of boys, B = 4/6 × 42
Number of boys, B = 4 × 7
Number of boys, B = 28 students.
Similarly, we we would have to multiply the total number of students by the fraction representing only the number of girls as follows:
Number of girls, G = 3/9 × Total number of students
Number of girls, G = 3/9 × 42
Number of girls, G = 1/3 × 42
Number of girls, G = 42/3
Number of girls, G = 14 students.
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Complete Question:
A class has 42 students. It can be determined that 3/9 are boys and 4/6 are girls, how many boys and girls are there in the class?
If A and B are supplementary angles and A is nine times as large as B, find the measures of A and B.
Supplementary angles add up to 180°
A+ B = 180
A is 9 times as large as B.
A = 9B
We have the system of equations:
A+ B = 180
A = 9B
Put the second equation into the first one, and solve for B
(9B)+ B = 180
10B = 180
B= 180/10
B = 18
Replace the value of B on any equation and solve for A:
A = 9B
A= 9(18)
A= 162
A= 162°
B=18°
Sarah wanted to lose some weight, so she planned a day of exercising. She spent a total of 4 hours riding her bike and jogging. She biked for 35 miles and jogged for 6 miles. Her rate for jogging was 10 mph less than her biking rate. What was her rate when jogging?
Consider the relation,
[tex]\text{Speed}=\frac{\text{ Distance}}{\text{ Time}}[/tex]The total time taken by Sarah for biking and jogging is 4 hours.
Given that her speed for biking was 10 mph, the time taken to bike 35 miles is calculated as,
[tex]\begin{gathered} T_b=\frac{35}{10} \\ T_b=3.5\text{ hours} \end{gathered}[/tex]So, out of the total 4 hours of exercise, Sarah spent 3.5 hours riding her bike.
The remaining 0.5 hour must have been spent on jogging,
[tex]undefined[/tex]What is the probability of rolling a 2 or a 3 when rolling a fair six-sided die?
Answer:
It would be a 2/6 chance, or a 1/3 chance.
Step-by-step explanation:
If 1 is divided by a number, the quotient is less than the number.If 1 is divided by -2, the result is (enter your response here), which is (your response) -2. A. greater than B. Less thanC. Equal to
Let us revise an important note
Positive numbers are increasing from 0 to positive infinity
Negative numbers are increasing from negative infinity to 0
If we divide 1 by 2, then the answer is 1/2 which is less than 2
That means the quotient is less than the divisor
If we divide 1 by -2, then the answer is -1/2 which is greater than -2
That means the quotient is greater than the divisor
Then the answer is
The result is greater than the number
The answer is A
which of the following properly describes "slope"? select all that apply. A. y2 - y1/ x2 - x1 B. x2-x1/y2-y1 C. run/rise D. rise/run E. ratio of change in y values (rise) for a segment of the graph to the corresponding change in x values (run)
The formula to calculate the slope is
[tex]m=\frac{y2-y1}{x2-x1}[/tex]A is right
also, the slope can be calculated with rise and run
[tex]m=\frac{rise}{run}[/tex]the correct formula is D.
and also apply E
the answer will be A,D and E
A random survey of 10 students recorded their number of hours of activity each week and their Body Mass Index (BMI). The results are shown in the table below. Student Body Mass Number of Hours of Activity Each Week Index Which of the following best describes the data? O linear positive association linear negative association no association O non-linear association
According to the given table, the dataset does not describe a linear-relationhip because they do not show a linear relation between the variables, they are too far away from each other.
Hence, the answer is D.Describe how to go from 1. The computer store A to the food store B.2. the computer store A, to the hardware store C.3. The hardware store C, to the food store B.Use words like left, right, up, down, north, south, east, and west. Each square on the coordinate plane is a city block.
Explanation
In the question, we are required to go through the image and describe how to move in the given directions. The solution can be seen below.
Number 1: The computer store A to the food store B.
Answer: In this case, the individual would move down for 6 city blocks
Number 2: The computer store A, to the hardware store C.
Answer: In this case, the individual will move down for one block then move right for 5 blocks
Number 3: The computer store A, to the hardware store C.
Answer: In this case, the individual will move down for five blocks and move left for 5 blocks
If r is the nominal rate and n is the number of times interest is compounded annually, then R=(1+r/n)^(n)-1 is the effective rate. Here, R represents the annual rate that the investment would earn if simple interest were paid. Use this formula to determine the effective rate for $1 invested for 1 year at 4.8% compounded semiannually.
Effective Rate in Compound Interest
Given r as the nominal rate of investment and n the number of times the interest is compounded annually, the formula for the effective rate is:
[tex]R=\mleft(1+\frac{r}{n}\mright)^n-1[/tex]We are required to find the effective rate for a rate of r=4.8% compounded semiannually. This means the value of n is 2 since there are two periods where interest is added to the principal per year.
Substituting the given values in the formula (recall r must be used as a decimal value, i.e. r=4.8/100=0.048):
[tex]R=(1+\frac{0.048}{2})^2-1[/tex]Calculating:
[tex]R=(1.024)^2-1=0.048576[/tex]The effective rate is 4.86%
Find the slope and the x- & y-intercepts of x + 2y = 6(5 pts) (Show work for finding X- & y-intercepts)
First, we need to write our equation in standard form — the y should be on the left- hand - side and the x should be on the right- hand side.
The first step is to subtract x from both sides, doing this we get:
[tex]2y=6-x[/tex]Now we divide both sides of the equation by 2 (this isolates the y on LHS), doing this gives us:
[tex]y\text{ = }\frac{6-x}{2}[/tex]which can also be written as
[tex]y=\frac{-x}{2}+3[/tex]The y-intercept is the point at which the line described by our equation intersects the y-axis. This intersection happens when x = 0; therefore, the y-intercept is
[tex]y=\frac{-0}{2}+\text{ 3}[/tex][tex]y=0\text{.}[/tex]The x-intercept is the point at which the line intersects the x-axis. This happens when y =0; therefore, the x-intercept is
[tex]0=\frac{-x}{2}+3[/tex][tex]-3\text{ = }\frac{-x}{2}[/tex][tex]x\text{ = 6.}[/tex]Now we see that the slope of the equation is -1/2 (the coefficient of x ). The y-intercept is y = 3 and the x-intercept is 6.
To the nearest hundredth, what is the value of x? X 40°
The given triangle is a right angle triangle,
Apply the trignometry ratio of tan
[tex]\tan \emptyset=\frac{Perpendicular}{Base}[/tex]From the given figure we have,
Perpendicular=x and base=72 and angle =40 degree
[tex]\begin{gathered} \tan 40^{\circ}=\frac{x}{72} \\ 0.839=\frac{x}{72} \\ x=0.839\times72 \\ x=60.408 \\ x=60.41 \end{gathered}[/tex]So the value of x is 60.41
f(x+h)-f(x)
h
lim:
h→0
i) The average rate of change of f(x) over the interval [x, x + h]
ii) The slope of the line tangent to f(x) at the point (x, f(x))
iii) The slope of the line secant to f(x) over the interval [x, x + h]
iv) The derivative of f(x)
O A. ii and iii
O B. i and iii
O c. ii
OD. i
...
O E.
i and iv
O F. ii and iv
Answer: F
Step-by-step explanation:
(i) The interval is meant to have infinitesimal width because the limit is approaching 0.
(ii) This gives the derivative at [tex](x, f(x))[/tex], which is the same as the slope of the tangent line.
(iii) False, this deals with the tangent line, not the secant.
(iv) True by definition.
What is the mean of 3x, 4x - 5 and 2x - 1?
Graph the reflection of the polygon in the given line #5 Y=2
We have the next image
the line of reflection is the line in red
the original polygon ABCD is the one in blue
the reflected polygon A'B'C'D' is the one in green
Angles A and B are supplementary angles. The measure of angle A is
73∘
What is the measure of angle B?
Answer:
17
Step-by-step explanation:
73+b=90
b=90-73
b=17
Use the figure below to find the value of x. (x + 20) y (x + 10° (y – 40)
Answer:
The value of x is 75;
[tex]x=75[/tex]Explanation:
From the diagram;
[tex](x+20)^0+(x+10)^0=180^0[/tex]Reason; supplementary angles.
Solving the equation, we have;
[tex]\begin{gathered} x+x+20+10=180 \\ 2x+30=180 \\ 2x=180-30 \\ 2x=150 \\ x=\frac{150}{2} \\ x=75 \end{gathered}[/tex]Therefore, the value of x is 75;
[tex]x=75[/tex]Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain. Given: XN NZ and NY = NW No; you cannot determine that the quadrilateral is a parallelogram. Yes; opposite sides are congruent. Yes; two opposite sides are both parallel and congruent. Yes; diagonals of a parallelogram bisect each other.
A parallelogram is a quadrilateral that has the following characteristics:
The opposite sides are parallel and congruent.
The opposite angles are congruent.
The consecutive angles are supplementary.
If any one of the angles is a right angle, then all the other angles will be at right angle.
The two diagonals bisect each other.
Since:
[tex]XN\cong NZ;NY\cong NW[/tex]We can conclude that the answer is:
Yes; diagonals of a parallelogram bisect each other.
A credit card bill for $562 was due on September 14. Purchases of $283 were made on September 19, and $12 was charged on September 28. A payment of $350 was made on September 25. The annual interest on the average daily balance is 19.5%. Find the finance charge due (in dollars) on the October 14 bill. (Use 365 for the number of days in a year. Round your answer to the nearest cent.)
The annual interest on a daily basis with 19.5%, then the finance charge due on October 14 will be $623.
What is interest?In the fields of finance and economics, interest is the payment made at a set rate by a borrower or deposit-taking financial institution to a lender or depositor in excess of the principal amount (the amount borrowed).
So, the finance charge will be;
(+) $ 562 due on sep 14, $ 562 x (19.5 x31) / (100 x 365) = $ 9.20
(+) purchase $ 283 on Sep 19, $ 283 x (19.5x26 ) / (100 x365) = $ 2.42
(+) finance charge on sep 28, $ 18 x(19.5 x17 ) / (100 x 365) = $ 0.17
(-) Repayment on 25 sep , $ 250 x (19.5 x20 ) / (100 x 365) = (2.745)
Finance charges from 14 sep to 14 oct will be $ 9.7= appr. 10
The Amount due on 14 October = $562 +$283 +$15+$11.855- $250
= $ 623
Therefore, The annual interest on a daily basis with 19.5%, then the finance charge due on October 14 will be $623
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Can you help to solve for number 5. Solving for X.
We will work at first with the small triangle ADC
[tex]m\angle DAC+m\angle C=m\angle ADB[/tex]mm[tex]m\angle DAC=55-20=35^{\circ}[/tex]We will use the sine rule
[tex]\frac{65}{\sin35}=\frac{AD}{\sin 20}[/tex]By using the cross multiplication
[tex]\begin{gathered} AD\times\sin 35=65\times\sin 20 \\ AD=\frac{65\sin 20}{\sin 35} \end{gathered}[/tex]In triangle ABD
We will use
[tex]\sin 55=\frac{x}{AD}[/tex]Then
[tex]x=AD\sin 55[/tex]Substitute AD by its value above
[tex]undefined[/tex]Kyree needs to fill up his truck with gasoline to drive to and from school. Gas costs $2.79 per gallon, and his truck holds a maximum of 28 gallons.Domain:Range:
Let x represent the cost per gallon of gasoline.
Let y or f(x) represent the cost of x gallons of gasoline.
Given that the cost per gallon is $2.79,
The function would be
f(x) = 2.79x
The domain refers to all possible values of x that can fit into the function. Given that the truck holds a maximum of 28 gallons, the maximum value of x is 28. When the truck is empty, the minimum value of x is 0. Therefore, the domain is 0 to 28
The range refers to all possibel values of y or f(x) that can satisfy the function.
When x = 0, f(x) = 2.79 * 0 = 0
When x = 28, f(x) = 2.79 * 28 = 78.12
The range would be 0 to 78.12
Domain: 0 to 28
Range: 0 t0 78.12
How many 7 digit phone numbers can be created if the first digit cannot be a zero, and the lastnumber must be an odd number?
Given:
Number of digits = 7
The first digit cannot be zero
Last number = odd number
The possible numbers between other than zero is 9
and there are 5 odd numbers.
Hence, the number of possible combinations is:
[tex]\begin{gathered} =\text{ 9 }\times\text{ 10 }\times\text{ 10 }\times\text{ 10 }\times\text{ 10 }\times\text{ 10 }\times\text{ 5} \\ =\text{ 4500000} \end{gathered}[/tex]Answer: Option A
The school band bought cheese and pepperoni pizzas in the ratio represented in the tape diagram for their end of year party. Based on the ratio how many pepperoni pizzas did they buy if they bought 12 cheese pizzas?
The cheese pizza is represented by 3 rectangles while the pepperoni pizza is represented by 1 rectangle.
Therefore, the ratio of cheese to pepperoni pizza is:
3 : 1
This means that if there are 3 cheese pizzas, then there will be 1 pepperoni pizza
Therefore, since they bought 12 cheese pizzas, it means that:
CCC + CCC + CCC + CCC = 12 cheese pizzas ( where C is cheese)
P + P + P + P = 4 pepperoni pizzas ( where P is pepperoni)
Thus, they bought 4 pepperoni pizzas
I'm not sure what to do for this question I have already tried could you help me with this?
1) Take into account that a linear relation can be written as follow:
y = mx + b
where m is the slope of the line and the constant b the y-coordinate of the y-intercept.
Due to Rocco started to count from a distance of 4 miles, this is a constant number, which is equivalent to b, that is, b = 4.
If the constant rate of the walk is 3 miles per 2 hours, then, m = 3/2 (because the slope is also a constant rate of change).
Then, you have the following linear equation for the relation between the distance traveled by Rocco and the time.
y = 3/2*x + 4
y is the number of miles of the Rocco walking
x is the time (in hours) he takes for the walking
2) Now, based on the previous equation, you have for the table:
3) The relation between the given variables is proportional because a change in x makes that y changes too.
The distance traveled by Rocco is given by the value of y when x = 4. As you can notice on the table, such a distance is 10 miles.
4 Evaluate: 2 (1) - O 1 16 2 ( ) V2 O O 1 2
To answer this question, we need to apply the following rule:
[tex]x^{-m}=\frac{1}{x^m}[/tex]This rule is known as the negative exponent rule. We also need to remember that when we have an exponent of 1/2 is the same as finding the square root for a number. Then, we have:
[tex](\frac{1}{4})^{-\frac{1}{2}}=\frac{1}{(\frac{1}{4})^{\frac{1}{2}}}=\frac{1}{\frac{\sqrt[]{1}^{}}{\sqrt[]{4}}}[/tex]Therefore, we have:
[tex]\frac{1}{\frac{1}{2}}=2[/tex]Thus, we have that:
[tex](\frac{1}{4})^{-\frac{1}{2}}=2[/tex]In summary, the correct answer is 2 (second option).
question 18:Evaluate: summation from n equals 2 to 8 of 12 times 4 tenths to the n plus 1 power period Round to the nearest hundredth. (1 point)
Given:
[tex]\sum_{n\mathop{=}2}^812(0.4)^{n+1}[/tex]Required:
Sum of the numbers
Explanation:
Let
[tex]A_n=\sum_{n\mathop{=}2}^812(0.4)^{n+1}[/tex]when n = 2, Aₙ becomes
[tex]A_2=12(0.4)^{2+1}=12\times(0.4)^3=0.768[/tex]when n = 3, Aₙ becomes
[tex]A_3=12(0.4)^{3+1}=12\times(0.4)^4=0.3072[/tex]when n = 4, Aₙ becomes
[tex]A_4=12(0.4)^{4+1}=12\times0.4^5=0.12288[/tex]
when n = 5, Aₙ becomes
[tex]A_5=12(0.4)^{5+1}=12\times0.4^6=0.049152[/tex]when n = 6, Aₙ becomes
[tex]A_6=12(0.4)^{6+1}=12\times0.4^7=0.0196608[/tex]when n = 7, Aₙ becomes
[tex]A_7=12(0.4)^{7+1}=12\times0.4^8=0.007866432[/tex]when n = 8, Aₙ becomes
[tex]A_8=12(0.4)^{8+1}=12\times0.4^9=0.003145728[/tex]So now,
[tex]\begin{gathered} A=A_1+A_2+A_3+A_4+A_5+A_6+A_7+A_8 \\ \\ A=0.768+0.3072+0.12288+0.049152+0.0196608+0.00786432+0.003145728 \\ \\ A=1.277902848\approx1.28 \end{gathered}[/tex]Final answer:
The
0=9 means no solution one solution or infinite solution?
Answer:
no solution
Step-by-step explanation:
If you end up with a false equality, then the initial statement is false, meaning that there are no solutions.
The American Water Works Association reports that the per capita water use in a single-family home is 69 gallons per day. Legacy Ranch is a relatively new housing development. The builders installed more efficient water fixtures, such as low-flush toilets, and subsequently conducted a survey of the residences. Thirty-six owners responded, and the sample mean water use per day was 64 gallons with a standard deviation of 8.8 gallons per day.
At the .10 level of significance, is that enough evidence to conclude that residents of Legacy Ranch use less water on average?
What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
Reject H0: µ ≥ 69 when the test statistic is less than ____.
a. The decision rule for this question would be to reject the null hypothesis if test statistic is less than the critical value.
b. The test statistic is given as: -3.4091
What is the hypothesis?We have the null hypothesis as
h0 : μ ≥ 69
The alternate hypothesis is
H1 : μ < 69
a. The decision rule would be to reject the null if the test statistic is greater than the critical value
at α = 0.10 the degree of freedom = 36 - 1 = 35
the critical value is -1.306
The test statistic calculation
[tex]t =\frac{ x - u}{s/\sqrt{n} }[/tex]
[tex]t = \frac{64-69}{8.8/\sqrt{36} }[/tex]
t = -3.4091
The decision rule would be to Reject H0: µ ≥ 69 when the test statistic is less than -1.306.
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22 8(11 + 2r) = 126r + 3
8(11 + 2r) = 126r + 3
first open the parenthesis
88 + 16r = 126r + 3
88 - 3 = 126r - 16 r
85 = 110r
divide both-side of the equation by 110
85/110 = r
r= 17/22
Use the Distributive Property and partial
products to find 5 × 727
The required product of the given expression [tex]5\times727[/tex] is [tex]3635[/tex].
Distributive property is defined as sum of two or more addends is multiplied by a number gives the same result by multiplying each addends separately and add the products.
For example:
[tex]a\times (b+c)=a\times b + a\times c[/tex]
Partial product is defined as the product of each digit of a number is multiplied by each digit of other number separately.
Solving the expression using Distributive property and partial products:
[tex]5 \times 727 = 5 \times ( 700 + 27 )\\[/tex] {∵ [tex]727=700+27[/tex]}
Here, Applying the distributive property we get:
[tex]= 5 \times700 + 5 \times27\\ = 3500 + 135\\ = 3635[/tex]
Hence, the required value of the expression [tex]5\times727[/tex] is [tex]3635[/tex].
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The product of the 5×727 is 3635.
The definition of a distributive property states that when the sum of two or more addends is multiplied by a number, the results are the same whether the addends are multiplied individually or all at once. Like a×(b+c) = a × b + a × c.
The definition of a partial product is the result of multiplying each digit of one integer by each digit of the other number separately.
Given in question, 5 × 727
Using distributive property and partial product,
5 × 727 = 5 × (700 + 27)
= 5 × 700 + 5 × 27
= 3500 + 135
= 3635
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Forty percent of 90 is what number
90 represents the 100%
Let's call x to the number that represents the 40%
To find the 40%, we can use the next proportion:
[tex]\frac{90}{x}=\frac{100\text{ \%}}{40\text{ \%}}[/tex]Solving for x:
[tex]\begin{gathered} 90\cdot40=100\cdot x \\ \frac{3600}{100}=x \\ 36=x \end{gathered}[/tex]36 is 40% of 90
About how much more is the total weight of the pacific halibut and conger than the weight of the yellowfin tuna ? Explain
The weight of pacific halibut is 459 pounds and weight of yellowfin tuna is 387 pounds.
There is 72 pounds more is the total weight of pacific halibut than the yellowfin tuna.