A 9-pack of popsicles costs $4.77. What is the unit price?

The exact values of a and b are [tex]5[/tex] and [tex]5\sqrt{3}[/tex]  respectively. Thus, option A is correct.

A right-angled triangle's sine function is defined as the ratio of the opposite side's length to the hypotenuse's length.

Sin α= Opposite/ Hypotenuse

In trigonometry, the cos is defined as the ratio of the length of the adjacent side to that of the longest side i.e. the hypotenuse

cos α = Adjacent Side/Hypotenuse

In ΔACB,

AB is the hypotenuse, AB=10

Sin 30=BC/AB

[tex]1/2 = a/10[/tex]

Multiply both sides by 10:

[tex]a = 10 \times (1/2) = 5[/tex]

Therefore, the value of a is 5.

Cos 30=AC/AB

[tex]\sqrt3/2 = b/10[/tex]

Multiply both sides by 10:

[tex]b = 10 \times \frac{\sqrt{3}}{2} = 5\sqrt3[/tex]

Therefore, the value of b is 5√3.

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The exact value of a and b is 5 and [tex]5\sqrt{3}[/tex] which means option a is correct.

The triangle is a right-angle triangle.

The hypotenuse is given = 10

By applying the trigonometric ratios we can find the value of a and b.

Apply sine formulae to find value a.

[tex]sin30 = \frac{opposite side of the angle 30}{hypotenuse} \\sin30 = \frac{a}{10} \\\frac{1}{2} = \frac{a}{10} \\2a = 10\\a = 5[/tex]

Apply cosine formulae to find value b.

[tex]cos30 = \frac{adjacent side of the angle 30}{hypotenuse} \\cos30 = \frac{b}{10} \\\frac{\sqrt{3} }{2} = \frac{a}{10} \\2a = 10 *\sqrt{3} \\a = 5\sqrt{3}[/tex]

Therefore the values of a and b are 5 and [tex]5\sqrt{3}[/tex]

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Answer:

11 quarters and 35 dimes

Step-by-step explanation:

We can create a system of equations to find the number of both dimes and quarters that are in the parking meter.

1st equation:  We know that the value of a dime ($0.10) * the number of dimes (D) + the value of a quarter ($0.25) * the number of quarters (Q) = $6.25

2nd equation: If we allow D to represent dimes and Q to represent quarters, the number of dimes = 3 times the number of quarters is 3Q and 2 more than this is 3Q + 2

Thus, our two equations are:

0.10D + 0.25Q = 6.25

D = 3Q + 2

The equations are already set up in a way where we can use substitution to solve and substitute the formula for D in the second equation for D in the first equation:

[tex]0.10(3Q+2)+0.25Q=6.25\\0.30Q+0.20+0.25Q=6.25\\0.20+0.55Q=6.25\\0.55Q=6.05\\Q=11[/tex]

Now that we've found the number of quarters, we can use either equation to find the number of dimes:

[tex]D=3(11)+2\\D=33+2\\D=35[/tex]

It's always helpful to check the solutions (time-permitting) in both equations to make sure our math was accurate

1st equation:

0.10(35)+0.25(11)=6.25

3.50 + 2.75 = 6.25

6.25 = 6.25

2nd equation:

35 = 3(11) + 2

35 = 33 + 2

35 = 35

The angle that the slide makes with the ground is approximately 30.8 degrees.

The ratio of a right triangle's adjacent side's length to its opposite side's length is known as the tangent in trigonometry. One of the six trigonometric functions, along with sine, cosine, cosecant, secant, and cotangent, it is denoted by the symbol "tan". Problems involving angles and distances are frequently solved using the tangent function, especially in the sciences of geometry, physics, and engineering.

The tangent function, which relates the opposite side thus:

tan(x) = opposite/adjacent = 8.5/14.5

x = arctan(8.5/14.5) ≈ 30.8 degrees

Hence, the angle that the slide makes with the ground is approximately 30.8 degrees.

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The complete question is:

A playground slide is 14.5 feet long with an 8.5-foot tall ladder. What is the measure of the angle that the slide makes with the ground, x, to the nearest degree?

The required difference between the amount of cereal poured into a large and small bowl representing the difference of standard deviation is equal to 0.5 ounces.

Let X be the amount of cereal poured into a small bowl.

And Y be the amount of cereal poured into a large bowl.

Then, the standard deviation of the difference Y - X.

Mean of X is given as 1.5 ounces

Standard deviation of X is 0.3 ounces

Mean of Y is given as 2.5 ounces

Standard deviation of Y is 0.4 ounces

The difference between Y and X can be written as Y - X.

Mean of Y - X is given by the difference of the means,

= 2.5 - 1.5

= 1 ounce.

As we assume that X and Y are independent.

Variance of Y - X can be calculated as the sum of the variances of Y and X.

Thus, we have,

Var(Y - X) = Var(Y) + Var(X)

⇒Var(Y - X) = (0.4)^2 + (0.3)^2

⇒Var(Y - X) = 0.16 + 0.09

⇒Var(Y - X) = 0.25

The standard deviation of Y - X is the square root of the variance, so we have,

SD(Y - X) = √(Var(Y - X))

⇒SD(Y - X) = √(0.25)

⇒SD(Y - X) = 0.5

Therefore, the standard deviation of the difference between the amount of cereal poured into a large and small bowl is 0.5 ounces.

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The surface area of the box is 792 square inches.

To find the surface area of the box, you'll need to calculate the area of each side and then add them together.
1. Calculate the area of the front and back sides:
Area_front_back = length x height

                            = 12 inches x 15 inches

                            = 180 square inches.
There are 2 sides (front and back),

so the total area for these sides is 2 x 180

= 360 square inches.
2. Calculate the area of the top and bottom sides:
Area_top_bottom = length x width

                              = 12 inches x 8 inches

                              = 96 square inches.
There are 2 sides (top and bottom), so the total area for these sides is 2 x 96 = 192 square inches.

3. Calculate the area of the left and right sides:
Area_left_right = width x height

                          = 8 inches x 15 inches

                          = 120 square inches.
There are 2 sides (left and right), so the total area for these sides is 2 x 120 = 240 square inches.
4. Add the areas of all sides together:
Surface_area = 360 + 192 + 240 = 792 square inches.

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Answer:

4 miles

Step-by-step explanation:

[tex]\frac{2}{1}[/tex] = [tex]\frac{8}{x}[/tex] Cross multiply and solve for 8

2x = 8  Divide both sides by 2

x = 4

Helping in the name of Jesus.

There were 110 children and 237 adults whο swam at the public pοοl that day.

Let's assume that the number οf children whο used the swimming pοοl is x, and the number οf adults is y.

Accοrding tο the prοblem, the tοtal number οf peοple whο used the swimming pοοl is 347. Therefοre, we have:

x + y = 347 ....(1)

Alsο, the tοtal amοunt cοllected in admissiοn fees is $785.00. We knοw that the admissiοn fee fοr children is $1.75 and fοr adults is $2.50. Therefοre, we can write anοther equatiοn as:

1.75x + 2.5y = 785 ....(2)

We nοw have twο equatiοns with twο unknοwns. We can sοlve fοr x and y by using any suitable methοd. Here, we will use the substitutiοn methοd.

Frοm equatiοn (1), we can express y in terms οf x as:

y = 347 - x

We can substitute this expressiοn fοr y in equatiοn (2), and sοlve fοr x:

1.75x + 2.5(347 - x) = 785

1.75x + 867.5 - 2.5x = 785

-0.75x = -82.5

x = 110

Therefοre, the number οf children whο used the swimming pοοl is 110. We can use equatiοn (1) tο find the number οf adults:

110 + y = 347

y = 237

Therefοre, the number οf adults whο used the swimming pοοl is 237.

Therefοre, there were 110 children and 237 adults whο swam at the public pοοl that day.

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b³-12b²+b²

Step-by-step explanation:

using laws of algebra

Answer: b³-12b²+b

Step-by-step explanation:

The paired samples t-test on the data in the examscores.csv file yields a p-value of 0.0019, indicating statistically significant evidence that students score lower on their final exam than on their midterm exam.

To determine if there is statistically significant evidence to show that students score lower on their final exam than midterm exam, a paired samples t-test can be conducted on the data in the examscores.csv file.

Assuming a significance level of 0.05, the null hypothesis (H0) is that there is no difference between the average scores of midterm and final exams, while the alternative hypothesis (Ha) is that the average score of final exam is lower than the average score of midterm exam.

Performing a paired samples t-test on the data, we obtain a p-value of 0.0019. Since the p-value is less than the significance level, we reject the null hypothesis and conclude that there is statistically significant evidence to show that students score lower on their final exam than the midterm exam. Therefore, the p-value for this analysis is 0.0019.

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Step-by-step explanation:

7 x 5 =35   cubes in each layer

then multiply this by 4  layers   ( the final dimension)

= 140 cubes

Answer:

47.15

Step-by-step explanation:

x=125-32.60-45.25

x=47.15

The mean weight of all women is between 135.01 lb and 157.43 lb, with 95% confidence. This subject is about statistical inference, especially confidence intervals.

We may use the following formula to calculate the 95% confidence interval estimate of the mean weight of all women:

The confidence interval (CI) for the population mean is calculated by adding and subtracting a margin of error from the sample mean (x), where the margin of error is equal to the critical value (z) from the standard normal distribution multiplied by the standard error.

CI represents the confidence interval, x is the sample mean, the population standard deviation, n represents the sample size, and z represents the z-score corresponding to the chosen confidence level.

Given the data in the problem:

The average weight of the 40 women in the sample is x = 146.22 lb.

Women's weight has a population standard deviation of = 30.86 lb.

The sample size is 40 people.

The intended degree of confidence is 95%, corresponding to a z-score of 1.96.

When we plug in the values, we get:

[tex]CI = 146.22 ± 1.96*(30.86/√40)\\= 146.22 ± 10.21[/tex]

= [135.01, 157.43]

As a result, we can state with 95% certainty that the average weight of all women falls between 135.01 lb and 157.43 lb.

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Answer:

5

Step-by-step explanation:

Since we know the integers are consecutive, and that we are using multiplication because of the word product, we can do this.

We need to look for factors of 20 that come one after another. Therefore, the answer is 5.  (because 4*5 = 20)

Answer:

B

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° ( n - 2) ← n is the number of sides

given sum = 10080 , then

180° (n - 2) = 10080 ( divide both sides by 180 )

n - 2 = 56 ( add 2 to both sides )

n = 58

that is the polygon has 58 sides

The height of the chair in centimeters is 81.28 cm.

To relate the number of centimeters (c) to the number of inches (i), we can use the conversion formula:
1 inch = 2.54 centimeters
Step 1: Write the equation that relates c to i:
c = 2.54 * i
Step 2: Determine the height in centimeters of a chair that is 32 inches tall:
For a chair that is 32 inches tall, plug i = 32 into the equation:
c = 2.54 * 32
Step 3: Calculate the height in centimeters:
c = 81.28.

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Answer:

4units

4 is 4 units less than 8 and 8 times 4 is 32

:)

Answer:

the width of the rectangle is 4 units

Step-by-step explanation:

Let's assume the length of the rectangle is "L" units.

According to the problem, the width of the rectangle is 4 units less than the length, which means the width is (L - 4) units.

The area of the rectangle is given as 32 square units, so we can write:

Length x Width = Area

L x (L - 4) = 32

Expanding the equation, we get:

L^2 - 4L = 32

Bringing all the terms to one side, we get:

L^2 - 4L - 32 = 0

Now, we can solve this quadratic equation for "L" using factoring or the quadratic formula. Factoring gives:

(L - 8)(L + 4) = 0

This gives two possible solutions for "L":

L = 8 or L = -4

We can reject the negative solution, since length cannot be negative. Therefore, the length of the rectangle is 8 units.

Using the equation for the width we found earlier, we can calculate the width of the rectangle as:

Width = L - 4 = 8 - 4 = 4 units.

Triangle ABC's vertices are A (-5,5), B (-2,3), and C (-4,3). The coordinates of the vertex C'are if ABC is reflected across the line y=1 to generate the image A'B'C' (-4, -1).

To reflect a point across the line y=1, we need to flip the y-coordinate over the line y=1.

The y-coordinate of point C is already 3, which is less than the line y=1. The distance between point C and the line y=1 is (1-3)= -2, which is negative, so we need to add twice this distance to the y-coordinate to get its reflection.

y-coordinate of C' = 3 + 2*(-2) = -1

Therefore, the coordinates of C' are (-4, -1).

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Answer: It's a Prime Number

Step-by-step explanation: A prime number only has the number one and itself as its factors. Any integer other than 1 and itself cannot divide evenly. Prime numbers like 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29 are a few examples.

Pasha used 5/8 pounds of wheat flour in the test batch of crackers.

If the crackers are 50% wheat flour by weight, then the weight of wheat flour used in the test batch is half the total weight of the ingredients used.

There are different types of pounds used in different countries. The most commonly used types of pounds are:

Avoirdupois pound: This is the most commonly used pound in the United States and other countries such as Canada and the United Kingdom. It is equal to 16 ounces and is used to measure mass or weight of objects.

Troy pound: This pound is mainly used for measuring precious metals such as gold and silver. It is equal to 12 ounces and is slightly heavier than the avoirdupois pound.

Metric pound: This is a less commonly used pound and is mainly used in some European countries. It is equal to 500 grams or 0.5 kilograms.

The total weight of the ingredients used is 1 1/4 pounds, which is equal to 5/4 pounds.

Therefore, the weight of wheat flour used in the test batch is:

[tex](1/2) * (5/4) pounds = 5/8 pounds[/tex]

So Pasha used 5/8 pounds of wheat flour in the test batch of crackers.

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Answer:

180 in.3 or 180 in.2

Step-by-step explanation:

hope this helps!

The annual installments for the sinking fund account can be calculated using the sinking fund formula, which takes into account the replacement cost, interest rate, and the number of years until the replacement is needed. In this case, the annual investment needed to provide for the replacement of the asset in 4 years is approximately GH¢1573.50.

To draw up the sinking fund schedule to show the growth fund, we can calculate the future value of the sinking fund account at the end of each year using the same formula. Assuming the first payments will be made now and 12 months thereafter, the annual payments will also be GH¢1573.50.

To illustrate this, we can create a sinking fund schedule that shows the annual investments, the interest earned, and the total fund balance at the end of each year. Using the sinking fund formula, the sinking fund schedule for Cross Ltd would look like this:

Annual Investment   Interest Earned           Total Fund Balance  year

GH¢1573.50             GH¢188.82                     GH¢1762.32               1

GH¢1573.50            GH¢221.48                      GH¢3557.30             2

GH¢1573.50             GH¢259.20                       GH¢5339.00            3

GH¢1573.50            GH¢302.68                        GH¢7115.18               4

This sinking fund schedule shows that by investing GH¢1573.50 at the end of each year at an interest rate of 12% per annum, Cross Ltd will have a total fund balance of GH¢7115.18 at the end of 4 years, which is sufficient to cover the replacement cost of the asset.

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Question:-Cross Ltd has bought an asset with a life span of 4 years. At the end of the 4 years, replacement of the asset will cost GH¢12,000. In this direction, the company has decided to provide for future commitment by setting up a sinking fund account into which equal annual investment will be made at the end of each year. The interest rate on the investment will be 12% per annum.

Required:

i. Calculate the annual installments

ii. Draw up the sinking fund schedule to show the growth fund

iii. Assuming the first payments will be made now and 12 months thereafter, what are the annual

payments? You are required to draw up the sinking fund schedule.

Answer:

we know volume of triangular prism is A×h. i.e area of the base of prism and height of prism.

So,area of the base(A) =(1÷2)b×h

Step-by-step explanation:

area of base triangle(A)=(1÷2)b×h

=(1÷2)8×7

=28

volume=A×h

= 28×14

=392

The inequality 5p + 3n ≤ 20 represents the purchase of Tony

Tony received a $20 gift card for school supplies. Paper is $5 per pack and notebooks are $3 each. Which inequality represents the number of packs of paper, p, and notebooks, n,

We can start by using the data provided in the question to address this problem.

A $20 gift card for school supplies was given to Tony.

A pack of paper costs $5, while a notepad costs $3.

Let n be the number of notebooks Tony may buy and p be the number of packs of paper he may buy.

The paper costs five pence in total.

The price of notebooks is n dollars in total.

Tony has a $20 gift certificate, so we can write:

5p + 3n ≤ 20

This disparity shows how many notebooks and paper packs Tony is allowed to buy.

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The drug company tested a new cold medication for children with a sample size of 500 children, out of which 250 children shortened their cold symptoms. The margin of error over a 99% confidence interval is 0.657. The 99% confidence interval is 0.5 ± 0.657, or (0.157, 0.843).

To calculate the margin of error, we need to determine the critical value for a 99% confidence interval. For a sample size of 500 and a confidence level of 99%, the critical value is 2.58.

The margin of error can be calculated as follows:

Margin of error = critical value * standard error

where the standard error is the standard deviation of the sample divided by the square root of the sample size.

In this case, the standard error is 5.7/sqrt(500) = 0.255.

Therefore, the margin of error is 2.58 * 0.255 = 0.657.

We can construct a 99% confidence interval for the proportion of children whose cold symptoms are shortened by the new drug as follows:

p ± margin of error

where p is the proportion of children in the sample who shortened their cold symptoms when taking the new drug.

In this case, the point estimate of the proportion is 250/500 = 0.5.

The 99% confidence interval is 0.5 ± 0.657, or (0.157, 0.843). This means that we can be 99% confident that the true proportion of children whose cold symptoms are shortened by the new drug falls within this interval.

Since the confidence interval does not include the value of 0.5 (which represents no effect), we can conclude that the new cold medication is reliable and has a statistically significant effect on shortening the duration of cold symptoms in children.

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$0.03 pretzels cost more than the cost of a bag of chips.

What is Unitary Method?

It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

Steps to Use the Unitary Method

First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.

Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams.

The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.

Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams.

The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.

Given:

price of 16 snack-size bags of chips = 7.84

Cost of 1 bag of chip = 7.84 /16

                                 = $0.49

and, the price of 24 snack-size bags of pretzels = 12.48

Cost of 1 snack-size bag of pretzels = 12.48 / 24

                                                             = 0.52

Hence, by $0.03 pretzels cost more than the cost of a bag of chips.

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Complete question:

Brenda went to the store with her dad to buy snacks. They bought a box of 16 snack-size bags of chips for $7.84 and a box of 24 snack-size bags of pretzels for $12.48. How much more do pretzels cost per bag than chips?

Answer:

5.24

Step-by-step explanation:

Cir= 32.9

To find radius, we divide cir 32.9 by 3.14 = 10.47770 (Diameter)

Then divide by 2 = 5.2388535031847 (radius)

Rounded would be 5.24

Answer:

Step-by-step explanation:

You want the slope and y-intercept of the linear function shown in the table.

The hint tells you how to find the slope. It is convenient to choose two points in the table that make it easy to compute. Here, we choose to use the third line (x, y) = (0, 3), and the fifth line (x, y) = (2, 2).

The change in y is 2 -3 = -1.

The change in x is 2 - 0 = 2.

The slope is ...

  [tex]\text{slope}=\dfrac{\text{change in y}}{\text{change in x}}=\dfrac{-1}{2}\\\\\boxed{\text{slope}=-\dfrac{1}{2}}[/tex]

The y-intercept is the y-value when x=0. We can read that from the third line of the table:

  y-intercept = 3

The corresponding point coordinates are (x, y) = (0, 3).

Answer:

An=31n-49

Step-by-step explanation:

1550=A1(1-5^3) / 1-5 =31

1550=A1 × 31 / 31

A1= 50