Answer:
The length is 10 cm
Step-by-step explanation:
The area of a rectangle is found by
A = l*w
240 = 24*l
Divide each side by 24
240/24 = 24l/24
10 =l
The length is 10 cm
ASAP help please!
The Venn diagram represents probabilities associated with two events. A is the event that the student has a regular afterschool activity, and B is the event that the student comes to school by bus. What is the probability that the student has an after-school activity and does NOT come to school by bus?
Answer:
0.22
Step-by-step explanation:
Looking at the Venn Diagram,
the intersection "0.43" means coming via bus and having after-school activity.
"0.12" means students who does not come by bus and who does not have after-school activity.
Now, we want probability of "having after-school" activity (the area A) but NOT COMING VIA BUS (area outside B).
We want the area outside B but within A.
That area is labeled 0.22
Hence,
The probability that the student has an after-school activity and does NOT come to school by bus is 0.22
A class of 24 students is having a drawing. Each student's name is placed on a piece of paper and then placed in a hat. One name is randomly drawn from the hat.
If there are 12 boys in the class, what is the probability that the name drawn is a girl's?
A. 1/2
B. 11/24
C. 11/12
D. 13/24
The probability of drawing a girl's name from a hat with 24 students of which 12 are boys is 1/2 or 50%.
The question is regarding the probability that a randomly drawn name is a girl's if there are 24 students in a class with 12 boys. Since the number of girls must be 24 total students minus 12 boys, which leaves us with 12 girls, the probability of drawing a girl's name is the number of girls over the total number of students. Therefore, the probability is 12 girls divided by 24 students, which simplifies to 1/2.
Which polynomials are in standard form?
Choose all answers that apply:
5 – 20
® 24 – 8x2 – 16
©
523 + 4x4 – 32 +1
0
None of the above
Answer:
None of the above
Step-by-step explanation:
None of the above polynomials are in standard form.
The fish population of Lake Collins is decreasing at a rate of 5% per year. In 2001 there were about 1,200 fish. Write an exponential decay function to model this situation. Then find the population in 2006.
The student's question involves creating an exponential decay function to determine the fish population in Lake Collins after five years, given a starting population in 2001 and a 5% annual decrease. The function is N(t) = 1200e^-rt, with r being 0.05 and t being 5. The estimated fish population for the year 2006 is approximately 935.
The student is asking for an exponential decay function to model the decrease in the fish population at Lake Collins. We are given that in 2001, there were about 1,200 fish, and the fish population is decreasing at a rate of 5% per year. To model this situation, we use the exponential decay formula:
N(t) = N0e-rt
Where:
N(t) is the fish population at time tN0 is the initial fish populationr is the decay rate (as a decimal)t is the time in years since the initial countFor this problem, the initial population N0 is 1,200, the decay rate r is 0.05 (since 5% is 0.05 as a decimal), and the time t we are interested in is 2006 - 2001 = 5 years. Plugging these values into the formula, we get:
N(5) = 1200e-0.05 * 5
Calculating N(5), the fish population in 2006, using the above formula:
N(5) = 1200e-0.25 ≈ 1200 * 0.7788 ≈ 935
Therefore, the estimated fish population in Lake Collins in 2006 would be approximately 935 fish.
April rewrote a quadratic function in vertex form.
h(x) = 5x2 – 30x + 30
Step 1: h(x) = 5(x2 - 6x+ + 30
Step 2: h(x) = 5(x2 - 6x + 9) + 30 – 45
Step 3: h(x) = 5(x - 3)2 + 15.
April said that the vertex is (3, 15). Is April correct?
April correctly transformed the quadratic function into vertex form, and the resulting vertex is (3, 15), as determined by the completion of the square method.
Explanation:April is indeed correct about the vertex of the function h(x). The vertex form of a quadratic function is h(x) = a(x - h)^2 + k, where the point (h, k) is the vertex of the parabola. April has rewritten the quadratic function h(x) = 5x^2 - 30x + 30 into vertex form as h(x) = 5(x - 3)^2 + 15, indicating that the vertex is at (3, 15). This can be verified through the completion of the square method, where a perfect square trinomial is created by adding and subtracting the appropriate constant term. April added and subtracted 9 inside the parentheses, which is (6/2)^2, to keep the equation equivalent. Finally, she factored out the coefficient of the quadratic term (5) before completing the square, which is correct.
What is the equation of the line?
Answer:
y=(1/4)x-3
Step-by-step explanation:
To find the equation of a line, use the following equation:
y=mx+b where m is the slope (rise/run) and b is the y-intercept.
The slope of the line is 1/4 and the y-intercept is -3. Just fill it into the problem to get the answer y=(1/4)x-3. Hope this helps! :)
Which expression shows partial quotients of 96 divided by 4?
20 plus 4
10 plus 4
20 plus 2 plus 1
10 plus 10 plus 3
Answer:
20 plus 4
please mark me brainliest
Step-by-step explanation:
20 plus 4 is the expression shows partial quotients of 96 divided by 4.
Here, we have,
given that,
Which expression shows partial quotients of 96 divided by 4.
now, we get,
96 divided by 4
i.e. 96/4
=24
as we know that,
24 = 20 + 4
so, we get,
24 equals 20 plus 4
i.e. 96 divided by 4 equals 20 plus 4.
Hence, 20 plus 4 is the expression shows partial quotients of 96 divided by 4.
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Which correctly describes a cross section of the right rectangular prism if the base is a rectangle measuring 15 inches by 8 inches? Select three options.. A right rectangular prism with length 15 inches, width of 8 inches, and height of 6 inches. A cross section parallel to the base is a rectangle measuring 15 inches by 8 inches. A cross section parallel to the base is a rectangle measuring 15 inches by 6 inches. A cross section perpendicular to the base through the midpoints of the 8-inch sides is a rectangle measuring 6 inches by 15 inches. A cross section perpendicular to the base through the midpoints of the 8-inch sides is a rectangle measuring 4 inches by 15 inches. A cross section not parallel to the base that passes through opposite 6-inch edges is a rectangle measuring 6 inches by greater than 15 inches. i will give brainly.
The statements which correctly describes a cross section of the right-rectangular prism if the base is a rectangle measuring 15 in. by 8 in. are: B, D and F.
The surface area of a rectangular prism.Mathematically, the surface area of a right-rectangular prism is calculated by using this formula:
A = 2(wl + hl + hw)
Where:
A is the surface area.l is the length.w is the width.h is the height.Based on the surface area of this right-rectangular prism, we can deduce the following points:
A cross-sectional area that is parallel to the base is a rectangle which measures 15 inches by 8 inches.A cross-sectional area that is perpendicular to the base through the midpoints of the 8-inch sides is a rectangle whch measures 6 inches by 15 inches.A cross-sectional area that is not parallel to the base and passes through opposite 6-inch edges is a rectangle whch measures 6 inches by greater than 15 inches.Read more on rectangular prism here: brainly.com/question/3867601
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The top of the lid to a small container is in the shape of a square with a side length of 6 centimeters, as shown. What is the
area of the top of the lid?
Use the formula for the area of a square, A-s. Where Arepresents the area and s represents the side length
O 12 cm
O 24 cm?
O 36 cm
72 cm
Given:
The top of the lid to a small container is in the shape of a square with a side length of 6 centimeters.
We need to determine the area of the top of the lid.
Area of the top of the lid:
The area of the top of the lid can be determined using the formula,
[tex]A=s^2[/tex]
where s is the side length of the square
Substituting [tex]s=6[/tex] in the above formula, we get;
[tex]A=6^2[/tex]
[tex]A=36[/tex]
Therefore, the area of the top of the lid is 36 cm²
Hence, Option C is the correct answer.
this is extremely hard and im not very smart:(
Answer:
The answer is B.
Step-by-step explanation:
The picture shows a right-angle triangle which is 90°. So you have to add up the expressions, in order to solve for x :
35° + 5x° = 90
Most married couples have two or three personality preferences in common. Myers-
Briggs used a random sample of 375 married couples and found that 132 had three
preferences in common. Another random sample of 571 couples showed that 217 had
two personality preferences in common. Find a 90% confidence interval for the
proportion of married couples with three personality preferences in common compared
with the proportion of couples with two preferences in common. (Show your confidence
in interval notation and show your interpretation, which was larger?
Answer:
The 90% confidence interval for the proportion of married couples with three personality preferences in common compared with the proportion of couples with two preferences in common is (-0.081, 0.025).
Step-by-step explanation:
The (1 - α)% confidence interval for difference in proportion formula is,
[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}[/tex]
The given information is:
n₁ = 375,
n₂ = 571,
X₁ = 132,
X₂ = 217.
Compute the sample proportion as follows:
[tex]\hat p_{1}=\frac{X_{1}}{n_{1}}=\frac{132}{375}=0.352\\\\\hat p_{2}=\frac{X_{2}}{n_{2}}=\frac{217}{571}=0.38\\[/tex]
For the 90% confidence level, the z-value is,
z₀.₀₅ = 1.645
*Use a z-table.
Compute the 90% confidence interval for the difference in proportion as follows:
[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}[/tex]
[tex]=(0.352-0.38)\pm 1.645\sqrt{\frac{0.352(1-0.352)}{375}+\frac{0.38(1-0.38)}{571}}\\=-0.028\pm 0.05256\\=(-0.08056, 0.02456)\\\approx (-0.081, 0.025)[/tex]
The 90% confidence interval for the proportion of married couples with three personality preferences in common compared with the proportion of couples with two preferences in common is (-0.081, 0.025).
This confidence interval implies that the true difference between the proportions lies in this interval with probability 0.90.
The 90% confidence interval for the difference in proportions of married couples with two and three personality preferences in common is (0.027, 0.089). This indicates that with 90% confidence, the proportion of couples with two preferences in common is significantly higher.
Explanation:Firstly, we need to find the proportions for both samples. The proportion for three personality preferences in common is 132/375 = 0.352 and for two personality preferences in common is 217/571 = 0.380.
Next, to compute the standard error, we use the formula √[ P(1 - P) / n ]. For three personality preferences we get √[ 0.352(1 - 0.352) / 375] = 0.026. And for two personality preferences we obtain √[ 0.380(1 - 0.380) / 571] = 0.021.
From these, the difference in the two sample proportions can be calculated, which is 0.380 - 0.352 = 0.028. The standard error of the difference can then be calculated as √( 0.026 ^ 2 + 0.021 ^ 2) = 0.033. At the 90% confidence level, the z-score is 1.645.
To calculate the confidence interval, note that 0.028 ± 1.645 * 0.033 is the equation we are trying to solve. This produces a range from 0.027 to 0.089.
So, the 90% confidence interval for difference in proportions is (0.027, 0.089), meaning that with 90% confidence, the proportion of couples with two preferences in common is significantly higher than those couples with three personality preferences in common.
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Madison claims that two data sets with the same median will have the same variability. Which data set would provide good support for whether her claim is true or false?
Her claim is true and she should use these data sets to provide support.
A box-and-whisker plot. The number line goes from 0 to 11. The whiskers range from 2 to 11, and the box ranges from 4 to 9. A line divides the box at 7.
A box-and-whisker plot. The number line goes from 0 to 11. The whiskers range from 2 to 11, and the box ranges from 4 to 9. A line divides the box at 6.
Her claim is true and she should use these data sets to provide support.
A box-and-whisker plot. The number line goes from 0 to 11. The whiskers range from 2 to 11, and the box ranges from 4 to 9. A line divides the box at 7.
A box-and-whisker plot. The number line goes from 0 to 11. The whiskers range from 2 to 11, and the box ranges from 5 to 8. A line divides the box at 7.
Her claim is false and she should use these to show that two data sets with the same median can have different variability.
A box-and-whisker plot. The number line goes from 0 to 11. The whiskers range from 2 to 11, and the box ranges from 4 to 9. A line divides the box at 7.
A box-and-whisker-plot. The number line goes from 0 to 11. The whiskers range from 2 to 11, and the box ranges from 5 to 8. a line divides the box at 7.
Her claim is false and she should use these to show that two data sets with the same median can have different variability.
A box-and-whisker plot. The number line goes from 0 to 11. The whiskers range from 2 to 11, and the box ranges from 4 to 9. A line divides the box at 7.
A box-and-whisker-plot. The number line goes from 0 to 11. The whiskers range from 2 to 11, and the box ranges from 5 to 8. a line divides the box at 5.5.
Answer:
A
Step-by-step explanation:
bruh
Answer:
C
Step-by-step explanation:
just my guess-
Find the roots of the factored polynomial.
(x + 6)(x + 3)
Answer:
x = -6 x=-3
Step-by-step explanation:
To find the roots, we set it equal to zero
(x + 6)(x + 3) =0
Using the zero product property
x+6 =0 x+3 =0
x = -6 x=-3
Answer:
x=-6,x=-3
Step-by-step explanation:
To solve this question we will have to solve one after another
(X+6)(x+3)
Let equate the equation to zero
So
(X+6)(x+3)=0
X+6=0
Substrate 6 from both sides
X=-6
X+3=0
Substrate 3 from both sides
x=-3
Therefore x=-6,x=-3
Samuel and Sebastian go to the movie theater and purchase refreshments for their friends.
Samuel spends a total of $36.75 on 1 bag of popcorn and 3 drinks.
Sebastian spends a total of $138.00 on 3 bags of popcorn and 12 drinks.
Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink.
Using these equations, determine and state the price of a drink, to the nearest cent.
Answer and Step-by-step explanation:
samuel---> 1pc+3dr=36.75
sebastian--->3pc+12dr=138
1pc+4dr=46
1pc+4dr=46
1pc+3dr=36.75
so 1 dr=46-36.75=$9.25
4dr is 9.25×4=37
so 1 pc=46-37=$9.00
Answer:
$9.25
Step-by-step explanation:
Cost of popcorn: x
Cost of drink: y
x + 3y = 36.75
x = 36.75 - 3y
3x + 12y = 138
x + 4y = 46
36.75 - 3y + 4y = 46
y = 46 - 36.75
y = 9.25
Find two numbers, if their sum is 93 and their difference is 9.
Answer:
51 and 42
Step-by-step explanation:
Use
x + y = 93
x - y = 9
Add those two equations together and you get 2x = 102
*y is not in the equation anymore because y + -y = 0*
Divide both sides by 2
x = 51
plug x into one of the equations; let's use x + y = 93
Then you get, 51 + y = 93
Subtract both sides by 51 and you get y = 42
Plug both in the other equation to make sure the numbers work.
51 + 42 = 93; true
51 - 42 = 9; true
Answer:
42 and 52
Step-by-step explanation:
the sum of 5 consecutive odd numbers is 505
Answer:
In a sequence of 5 numbers, the 3rd number is the middle number. So in your problem the third number is the average of the 5 numbers -- which is the sum of the numbers, divided by how many there are: 505/5 = 101.
Explanation:
The 5 numbers will be: 97, 99, 101, 103 and 105
Let the 5 consecutive numbers be x-4, x-2, x, x+2 and x+4.
Now it is given that the sum of the 5 numbers is 505. This can be represented mathematically as follows:
[tex](x-4)+(x-2)+x+(x+2)+(x+4) = 505\\\\5x = 505\\\\x= 101[/tex]
So, x - 4 = 97
x - 2 = 99
x + 2 = 101
x + 4 = 103
Thus, the 5 numbers will be: 97, 99, 101, 103 and 105
Steve decided to buy a box of pizza from another restaurant. The
restaurant is offering a square pizza and a round pizza. Round pizza
has an area of 49 pi square inches. The square pizza has an area of 49
square inches. Which box of pizza will Steve buy if he wants to eat
more crust? Explain your reasoning.
Show your work
Answer:
Round pizza
Step-by-step explanation:
Area of the Round Pizza =[tex]49 \pi[/tex] square inches.
Area of the Square Pizza = 49 square inches.
Recall that: [tex]\pi =\frac{22}{7}[/tex]
Therefore:
Area of the Round Pizza =[tex]49 \pi=49X\frac{22}{7}=154 \:Square \:Inches[/tex]
Since 154 is greater than 49(154>49)
If Steve wants to eat more crust, he will buy the round pizza.
Convert -18° to radians.
Answer: -(pi)/10 radians or D on Edge
Step-by-step explanation: correct answer on edge
x−1.27=4.09
What is x
How many ways can you write y^6 as the product of two powers?
Answer:
4
Step-by-step explanation:
Write y6 as a product of two powers with the same base in four different ways, using negative or zero exponents in each product.
Margo deposited $100 into a savings account earning 4.5% simple annual interest. At the end of each year, she adds $100 to her account. Fill in the table below to figure out how much money was in Margo's account at the end of 3 years.
Answer:
principal interest total money in account
at the end of year
Year one $100 $4.5 $104.5
year two $200 $ 9 +$4.5 $ 213.5
year three $300 $ 9 +$4.5 + $13.5 $ 327
Step-by-step explanation:
Simple interest for any principal is given by
I = p* r* t/100
I = interest rate accrued on principle amount
p is the amount deposited
r is the rate of interest
t is the time period of saving
_______________________________________________
For year one
p = $100
r = 4.5%
t=1
I = 100*4.5*1/100 = 4.5
_______________________________________________
For year two $100 more is added to already existing $100 in account.
p = 100 +100 = $200
r = 4.5%
t=1
I = 200*4.5*1/100 = 9
_______________________________________________
For year two $100 more is added to already existing $200 in account after two years.
p = 100 +100 +100 = $300
r = 4.5%
t=1
I = 300*4.5*1/100 = 13.5
_______________________________________________
There fore total money in Margo account is
$300 saving deposited by her
$4.5 + $9 + $13.5 = $27 (interest accrued in three time)
Formulating the results in tabular form
principal interest total money in account
at the end of year
Year one 100 4.5 104.5
year two 200 9 +4.5 213.5
year three 300 9 +4.5 + 13.5 327
I need help with slope.
Answer:
For #1, the slope is [tex]\frac{2}{2}[/tex], which could also be written as 1
For #2, the slope is [tex]\frac{1}{4}[/tex]
For #3, the slope is [tex]-\frac{2}{1}[/tex], which could also be written as -2
Step-by-step explanation:
Remember, [tex]\frac{rise}{run}[/tex]
Alice has two flying disks. One is 12 cm in diameter and the other is 24 cm in diameter. What is the difference between the areas of the two flying disks?
Answer:
432π cm² or 1356.48 cm²
Step-by-step explanation:
The area of a circle is πr²
The area of the disks are 144π and 576π.
576π-144π = 432π
432π ≈ 1356.48 cm²
To find the difference in areas of two circles, calculate the area of each circle using the formula πr² and then subtract the smaller area from the larger one. For Alice's discs with diameters 12 cm and 24 cm, the areas are 36π and 144π square cm respectively, and their difference is 108π square cm.
Explanation:To find the difference in the areas of Alice's two flying disks, first we need to calculate the area of each disk. The formula for the area of a circle (or disk) is πr², where r is the radius of the circle. The radius is half of the diameter, so for the first disk, the radius is 6 cm and for the second disk, the radius is 12 cm.
The area of the first disk is π*(6 cm)² = 36π square cm. The area of the second disk is π*(12 cm)² = 144π square cm. The difference between these two areas is 144π - 36π = 108π square cm.
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Which inequality best represents the following situation: The speed limit in your neighborhood is 30 miles an hour and you are not breaking the law.
Answer:
D
Step-by-step explanation:
You can drive anywhere less than or equal to 30 mph, and it'd be legal
Please help me answer this
Answer:
C
Step-by-step explanation:
for every value of x we put in the option the only function which satisfies the table of data is C
How can you record hundredths as fractions and decimals?
Hundredths as fractions and decimals is given below.
Step-by-step explanation:
When we write a decimal number, look at the decimal point first. If the last number is two places away from the decimal point, it is in the hundredths place. The number 0.39 would be written as thirty-nine hundredths. The nine is the last number and is in the hundredths place.First, convert the decimal to fraction using tenths, hundredths, thousandths, etc. depending on the number of decimal places. e.g. 1.75 = 1 75/100. Next, simplify the fraction part to the lowest common term. e.g. 75/100 = 3/4.5 hundredths is 5 over one hundred, 5 hundredths as a Fraction is 5/100. If you divide 5 by one hundred you get 5 hundredths as a decimal which is 0.05.To convert a fraction to decimal, we divide the numerator by the denominator using long division and to convert a fraction to percent, we convert the fraction to decimal and the decimal to percent. To convert a percent to decimal or fraction, we divide the percent by 100 and reduce the fraction.4 hundredths is 4 over one hundred, 4 hundredths as a Fraction is 4/100. If you divide 4 by one hundred you get 4 hundredths as a decimal which is 0.04.To learn more about this :
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There are 15 animals in a barn. These animals are horses and chickens. There are 44 legs in all. Write a system of equations that represents the situation and find out how many animals were horses and how many were chickens?
Final answer:
there were 7 horses and 8 chickens in the barn.
Explanation:
To represent the situation with a system of equations, let's assume that the number of horses is represented by 'h' and the number of chickens is represented by 'c'.
We know that there are a total of 15 animals, so we can write the equation: h + c = 15.
We also know that the total number of legs is 44, and since each horse has 4 legs and each chicken has 2 legs, we can write the equation: 4h + 2c = 44.
To solve this system of equations, we can use the method of substitution or elimination. Substituting h = 15 - c into the second equation, we get 4(15 - c) + 2c = 44. Simplify and solve for c to find the number of chickens, then substitute the value of c back into the first equation to find the number of horses.
Let's solve this system of equations:
h + c = 15
4h + 2c = 44
We can solve this using the method of substitution:
h = 15 - c
Substituting this into the second equation:
4(15 - c) + 2c = 44
60 - 4c + 2c = 44
-2c = 44 - 60
-2c = -16
c = -16/-2
c = 8
Substituting the value of c back into the first equation:
h + 8 = 15
h = 15 - 8
h = 7
So, there were 7 horses and 8 chickens in the barn.
Simplify each expression 8+7y-3y+2-4
Given f(x) = -10x + 45, find x when f(x) = 15.
Answer:
3 =x
Step-by-step explanation:
f(x) = -10x + 45
f(x) = 15
15 = -10x +45
Subtract 45 from each side
15-45 = -10x+45-45
-30 = -10x
Divide each side by -10
-30/-10 = -10x/-10
3 =x
PLZ HELP!!!!!!! WILL GIVE BRAINLIEST!!!
Answer:
Step-by-step explanation: