Sarah lost her science book. Her school charges a lost book fee equal to 75% of the cost of the book. Sarah received a notice stating that she owed the school $60 for he lost book. How much did the school pay for the book.

Answer:

We will need [tex]13\frac{1}{3}[/tex] quarts of white paint to mix with 4 quarts of blue paint to make the required shade of blue.

Step-by-step explanation:

A certain shade of blue is made by mixing [tex]1\frac{1}{2}[/tex] quarts of blue paint with 5 quarts of white paint. This means the ratio of quantity of blue paint to white paint is:

[tex]1\frac{1}{2}:5\\\\ \frac{3}{2}:5\\\\ 3:10[/tex]

If we want to prepare this certain shade then we have to maintain this ratio of blue paint to white paint.  We have 4 quarts of blue paint and we need to find how many quarts of white paint we need. Let the amount of white paint needed be x quarts. So ratio of blue to white will be 4 : x

Since, this ratio must be equal to 3 : 10, we can set both ratios equal and find the value of x

[tex]3:10 = 4:x\\\\\frac{3}{10}=\frac{4}{x}\\\\ 3x=40\\\\ x=\frac{40}{3}\\\\ x=13\frac{1}{3}[/tex]

This mean we will need [tex]13\frac{1}{3}[/tex] quarts of white paint to mix with 4 quarts of blue paint to make the required shade of blue.

6/5

Step-by-step explanation:

Answer:

4x^3 + 41x^2 +51x + 54

Step-by-step explanation:

This is a polynomial distribution

(x + 9 )(4x^2 + 5x + 6) We start by multiplying every term with x

4x^3 + 5x^2 + 6x there is plus sign between (x+9) so we put plus and start multiplying every term by 9

4x^3 + 5x^2 + 6x + 36x^2 + 45x + 54

4x^3 + 41x^2 +51x + 54

If we are looking for when they would be the same at a given time:

First, we need to set them to each other:

50 + 10x = 25 + 15x

Move them around and then get this:

25 = 5x

Divide by 5 from both sides

5 = x

Answer:

The answer to your question is  77/500    

Step-by-step explanation:

Data

decimal number = 0.154

fraction number = ?

Process

To convert a decimal number into a fraction, express the decimal number without the zero and the decimal point (this number will be the numerator) and write as a denominator a number one plus as many zeros after this number as numbers there are after the decimal point of the numerator.

Example

              0.154 has three number after the decimal point then we write 1000

                             154/1000 =

Simplify

                              77/500            

Answer:

Ruby pays a dollar every 12 messages.

Step-by-step explanation:

It costs Ruby $4 to send 48 text messages. To find the unit rate, you would divide 48 by 4. So the result would lead to 12 messages per dollar.

Answer:

[tex]a.\ P(C<8.0)=0.1587\\\\b. \ P(8.2<C<8.3)=0.1359\\\\c. 7.87\ oz[/tex]

Step-by-step explanation:

a. Let C be the normally distributed random variable.

-Given the chocolates is normally distributed with mean =8.1 oz and standard deviation =0.1 oz.

#The proportion of those less than 8.0 oz can be calculated as:

[tex]P(C<8.0)=P(Z<\frac{\bar X-\mu}{\sigma})\\\\\\=P(Z<\frac{8.0-8.1}{0.1})\\\\\\=P(Z<-1)=0.1587[/tex]

Hence, the proportion of bars weighing below 8 ounces is 0.1587 or 15.87%

b. We use the z-test to determine the probability or proportion of bars weighing between 8.2 and 8.3 ounces:

[tex]P(8.2<C<8.3)=P(\frac{\bar X-\mu}{\sigma}<Z<\frac{\bar X-\mu}{\sigma})\\\\\\=P(\frac{8.2-8.1}{0.1}<Z<\frac{8.3-8.1}{0.1})\\\\\\=P(1<Z<2)\\\\\\=0.9772-0.8413\\\\=0.1359[/tex]

Hence, the proportion of bars weighing between 8.2 and 8.3 ounces is 0.1359 or 13.59%

c. To label the wrappers such that only 1% are underweight.

#Find B such that

P(C<B)=0.01

#Now find z-value such that:

[tex]P(Z<B)=0.01[/tex]

Using the z-tables, z=-2.33

Therefore:

[tex]C=z\sigma +\mu\\\\=-2.333\times 0.1+8.1\\\\=7.8667\approx 7.87 \ oz[/tex]

Hence, the wrappers should be labelled as 7.87 ounces

Approximately 15.87% of the chocolate bars weigh less than 8.0 oz. Approximately 13.59% of the bars weigh between 8.2 and 8.3 oz. The wrappers should be labeled as 7.867 oz to ensure only 1% of the bars are considered underweight.

In order to answer the student's questions, we have to find the Z-scores, which correspond to the given weights, in the standard normal distribution table.

(A) To find the proportion of chocolate bars that weigh less than 8.0 oz, we first find the Z-score using the formula Z = (X-μ)/σ, where X is the weight, μ is the mean, and σ is the standard deviation. Thus, Z = (8.0-8.1)/0.1 = -1, implying the bar is one standard deviation below the mean. Referring to the Z-table, Z = -1 corresponds to 0.1587, or 15.87% of the population. Therefore, approximately 15.87% of the chocolate bars weigh less than 8.0 oz.

(B) To find the proportion of chocolate bars weighing between 8.2 and 8.3 oz, find the Z-scores for 8.2 and 8.3 oz. Using the Z-score formula, Z_8.2 = (8.2-8.1)/0.1 = 1 and Z_8.3 = (8.3-8.1)/0.1 = 2. From the Z-table, the proportions corresponding to these Z-scores are 0.8413 and 0.9772 respectively. Thus, the proportion between these weights is 0.9772 - 0.8413 = 0.1359, or 13.59%.

(C) For only 1% of the bars to be underweight, we need a weight that is at the 1% mark in the standard normal distribution. Looking up the Z-table, Z = -2.33 corresponds with the lower 1%. Using the Z = (X-μ)/σ formula rearranged to X = Z*σ + μ, we get X = -2.33*0.1 + 8.1 = 7.867 oz. Therefore, to ensure only 1% of bars are underweight, the wrappers should be labeled as 7.867 oz.

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Answer: 1 1/4

Step-by-step explanation:

Solving the fraction parts

3/8 + 7/8 = 10/8

Reducing the fraction part, 10/8

10/8= 5/4

Simplifying the fraction part, 5/4

5/4= 1 1/4

Answer:

10/8

Step-by-step explanation:

You add 7/8 + 3/8 and that equals 10/8

I hope that's helpful

Answer:

y = 5[tex]e^{tan(x)}[/tex]

Step-by-step explanation:

work in picture below

Answer:

B.- There is no vertical asymptote at x=0

E.- There is a removable discontinuity at x= -a

Step-by-step explanation:

Answer:

The above answers are correct! The correct options are B and E!

Step-by-step explanation:

Hope this helped confirm :)

Have a great day!

Answer:

(m - n ) = b

mn = c

The relationship between m and n is such that their product is c  and their difference is b

Step-by-step explanation:

roots are   x = -m   and  x = n

-m   =   -b/2 - root(b*b + 4c)/2

n = -b/2 + root(b*b + 4c)/2

(x + m)(x -n) =  x*x +(m - n)x  - mn

(m - n ) = b

mn = c

Sample Answer: The value of m must be greater than the value of n. When you multiply the binomials, the middle term is the result of combining the outside and inside products. So, bx = –nx + mx, or bx = (–n + m)x. This means that b = –n + m. When adding numbers with opposite signs, you subtract their absolute values, and keep the sign of the number having the larger absolute value. Since b is positive, m must have the larger absolute value.

its right ur welcome

Answer:

Step-by-step explanation:

Suppose m = 2 + 6i, and |m+n|=3√10,

The modulus sign means m+n can either be positive or negative as shown.

If it is positive:.2+6i+n = 3√10

n = 3√10-(2+6i)

n = 3√10-2-18√10i

n = (-2+3√10)+√10i

b) Example of the complex number is given as (-2+3√10)+√10i. This is a complex number because it contains the real part and the imaginary part.

Answer:

the radius

Step-by-step explanation:

4/3*pi*r squared

The circumference of a circle with a radius of 9 millimeters is approximately 56.54867 mm, or 57 mm when rounded to two significant figures.

The circumference of a circle can be calculated using the formula C = 2πr, where π (pi) is approximately 3.14159 and r is the radius of the circle. Given that the radius of the circle is 9 millimeters, we can plug this value into the formula to find the circumference.

C = 2 × 3.14159 × 9 mm

After calculating, the circumference (C) is 56.54867 mm. However, if we keep the significant figures consistent with the given radius, the circumference is approximately 57 mm.

The circumference of the circle with a radius of 9 millimeters is approximately 56.55 millimeters, calculated using the formula [tex]\(C = 2 \pi r\)[/tex].

The circumference (C) of a circle is calculated using the formula [tex]\(C = 2 \pi r\)[/tex], where r is the radius of the circle. Given that the radius (r) is 9 millimeters, substitute this value into the formula:

[tex]\[ C = 2 \pi \times 9 \][/tex]

Using an approximate value for [tex]\(\pi\)[/tex], which is 3.14159, the calculation is:

[tex]\[ C \approx 2 \times 3.14159 \times 9 \][/tex]

[tex]\[ C \approx 56.54867 \][/tex]

Therefore, the circumference of the circle with a radius of 9 millimeters is approximately 56.55 millimeters.

Answer:

The cost C as a function of t is C(t) = 30,000 + 6,400,000 t - 40,000 t²

Step-by-step explanation:

The function N(t) = 800 t -  5t², represents the number of cars produced at a time t hours in a day, where 0 ≤ t ≤ 10

The function C(N) = 30,000 + 8,000 N, represents the cost C​ (in dollars) of producing N cars

We need to find The cost C as a function of the time t

That means Substitute N in C by its function by other word find the composite function (C о N)(t)

∵ C(N) = 30,000 + 8,000 N

∵ N(t) = 800 t - 5 t²

- Substitute N in C by 800 t - 5 t²

∴ C(N(t)) = 30,000 + 8000(800 t - 5 t²)

- Multiply the bracket by 8000

∴ C(N(t)) = 30,000 + 8000(800 t) - 8000(5 t²)

∴ C(N(t)) = 30,000 + 6,400,000 t - 40,000 t²

- C(N(t) = C(t)

∴ C(t) = 30,000 + 6,400,000 t - 40,000 t²

The cost C as a function of t is C(t) = 30,000 + 6,400,000 t - 40,000 t²

The cost C as a function of time t of operation is given by the equation C(t) = 30000 + 6400000t - 40000t^2. This equation factors in the initial costs, the revenue from the cars produced, and the costs per each additional hour of operation.

To answer your question, we first need to find a relationship between the cost C(N) and the number of cars produced N(t) as a function of time. We know that N(t) = 800t - 5t2 and C(N) = 30000 + 8000N. We can substitute N(t) into C(N) to find C as a function of time t.

Therefore, the cost C as a function of time t, denoted as C(t), is C(t) = 30000 + 8000 * (800t - 5t2).

This simplifies further to C(t) = 30000 + 6400000t - 40000t2.

In other words, the cost of operations in the factory is a function of the time it operates, taking into account the initial costs, the revenue from the cars produced, and the cost associated with each additional hour of operation.

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Answer:

56.7% to one decimal place

Step-by-step explanation:

30 students

13 are boys

30-13=17

17 are girls

As a decimal 0.5667

As a percentage 56.67%

56.7% to one decimal place

Answer:

[tex] ME= z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

And replacing we got:

[tex] ME= 1.96 *\sqrt{\frac{0.37 (1-0.37)}{480}}= 0.0432[/tex]

And replacing into the confidence interval formula we got:

[tex]0.37 - 1.96 *\sqrt{\frac{0.37 (1-0.37)}{480}}=0.327[/tex]

[tex]0.37 + 1.96 *\sqrt{\frac{0.37 (1-0.37)}{480}}=0.413[/tex]

And the 95% confidence interval would be given (0.327;0.413).

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Solution to the problem

The confidence interval would be given by this formula

[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

Assuming a 95% of confidence. For the 95% confidence interval the value of [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2=0.025[/tex], with that value we can find the quantile required for the interval in the normal standard distribution.

[tex]z_{\alpha/2}=1.96[/tex]

The margin of error would be:

[tex] ME= z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

And replacing we got:

[tex] ME= 1.96 *\sqrt{\frac{0.37 (1-0.37)}{480}}= 0.0432[/tex]

And replacing into the confidence interval formula we got:

[tex]0.37 - 1.96 *\sqrt{\frac{0.37 (1-0.37)}{480}}=0.327[/tex]

[tex]0.37 + 1.96 *\sqrt{\frac{0.37 (1-0.37)}{480}}=0.413[/tex]

And the 95% confidence interval would be given (0.327;0.413).

Answer:

The tank can hold 4110.26 gallons of water.

Step-by-step explanation:

In order to solve this question we need to compute the volume of this tank, the volume is given by:

V = (area of the base)*height

Since the base is circullar, it is given by:

area of the base = pi*r^2

So we have:

V = height*pi*r^2

The radius of circle is the diameter divided by 2, so in this case r = 10/2 = 5 ft. We can now use the values on the equations:

V = 7*3.14*(5)^2 = 549.5 ft^3

Since each cubic foot holds 7.48 gallons of water the volume in gallons is:

V = 549.5*7.48 = 4110.26 gallons

The tank can hold 4110.26 gallons of water.

To find the number of gallons a cylindrical tank can hold, calculate the volume in cubic feet using the formula V = πr^2h, where the diameter is 10 feet (radius is 5 feet) and the height is 7 feet, then multiply the volume by 7.48 gallons per cubic foot.

To calculate the number of gallons a cylindrical tank can hold, we first need to find the volume of the cylinder in cubic feet and then convert that volume to gallons. The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.

Since the diameter of the tank is given as 10 feet, the radius (r) would be half of that, which is 5 feet. The height (h) is given as 7 feet. Plugging these values into the formula, we get:

V = π(5)^2(7) = π(25)(7) = π(175) cubic feet.

Using the conversion factor 7.48 gallons per cubic foot, we can find the total gallons the tank holds:

Gallons = Cubic feet × 7.48 gallons/cubic foot

Gallons = π(175) × 7.48 gallons/cubic foot

We thus calculate the total volume in gallons.

Answer:

Use the value for the variable to solve for the other unknowns.  Substitute the value for the variable into the expression for the number of seats on the middle level.  Substitute the value for the variable into the expression for the number of seats on the lower level.

Answer:

54mm

Step-by-step explanation:

50, 50, 52,53, 54, 55, 55, 55, 57

The theoretical probability of 3 students from your school being selected as contestants out of 9 possible contestant spots is 0.28

Explanation:

School students = 40

Total people = 130

Total contestant spot = 9

Probability of 3 contestant from school = ?

The number of combinations of 3 of the 40 students getting a spot = ⁴⁰C₃

The number of combinations of the other audience members filling the other 6 spots = ⁹⁰C₆

The number of 9 contestants with 3 students in them = ⁴⁰C₃ X ⁹⁰C₆

The total number of possible 9 contestants from the audience = ¹³⁰C₉

Probability of the group of contestants having 3 students = [tex]\frac{^4^0C_3 X ^9^0C_6}{^1^3^0C_9}[/tex]

Solving the equation further we get:

Probability of the group of contestants having 3 students = 0.28

Answer:

He should be very confident

Step-by-step explanation:

He should be very confident because he has a 7 out of 8 chance of getting a small medium or large prize and he has a 1 out of 8chance of getting nothing

The probability that the box selected will win the prize is A = 7/8 = 87.5 %

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability that the box selected will win the prize be A

Now , the total number of boxes = 8

The box which has a big prize = 1

The number of boxes which have medium prize = 3

The number of boxes which have small prizes = 3

So , the total number of boxes with prize = 7 boxes

And , probability that the box selected will win the prize A = total number of boxes with prize / total number of boxes

On simplifying , we get

The probability that the box selected will win the prize A = 7 / 8

The probability that the box selected will win the prize A = 0.875

Hence , the probability is 7/8

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Question:

Temperatures for 5 Days This Week and Last Week

Low Temperatures This Week (Degrees Fahrenheit) 4 10 6 9 6 Low Temperatures Last Week (Degrees Fahrenheit) 13 9 5 8 5 Which measures of center or variability are greater than 5 degrees? Select three choices.

a) the mean of this week’s temperatures

b) the mean of last week’s temperatures

c) the range of this week’s temperatures

d)the mean absolute deviation of this week’s temperatures

e) the mean absolute deviation of last week’s temperatures

Answer:

a) the mean of this week’s temperatures

b) the mean of last week’s temperatures

c) the range of this week’s temperatures

Step-by-step explanation:

I would be verifying the options a, b, and c in my answer above through calculations which are shown below.

We were given the following data:

Low Temperatures This Week (Degrees Fahrenheit)

4, 10, 6, 9, 6

Low Temperatures Last Week (Degrees Fahrenheit)

13, 9, 5, 8, 5

We are to find which measures of center or variability are greater than 5 degrees.

Option a

The mean of this week’s temperatures

(4+ 10+ 6+9+ 6) °F ÷ 5 = 35 °F ÷5 = 7°F

Option a is correct because it measures of center or variability which is 7 °F is higher than 5°F

Option b

The mean of last week’s temperatures

(13+ 9 + 5 + 8 + 5) °F = 40°F ÷ 5 = 8°F

Option b is correct , because its measure of variability which is 8°F is greater than 5°F.

Option c

the range of this week’s temperatures

This week's temperature is given as

(4, 10, 6, 9, 6) °F

Range is defined as the difference between the highest number and the lowest number

Range of this week's temperature = (10 - 4) °F = 6°F

Hence Option c is correct because it measures of center or variability which is 6°F is greater than 5°F

From the above calculations we can accurately confirm that options a, b, and c are correct because the measures of their center or variability is greater than 5°F

Answer:

A,B,C

Step-by-step explanation:

Answer:

Length = 12yards

Width = 14yards

Sum = 26yards

Step-by-step explanation:

Let assume the play ground is rectangular in form.

Area of a rectangle = length × width

Given area of the playground = 168yd²

If the width of the playground is 2yd longer than its length, then:

W = L+2

Substituting W = L+2 into the formula above we have:

A = L × (L+2)

A = L²+2L

168 = L²+2L

L²+2L-168 = 0

L²+14L-12L-168 = 0

L(L+14)-12(L+14) = 0

(L-12)(L+14) = 0

L-12 = 0 and L+14 =0

L = 12 and -14

Taking the positive length, L = 12yards

If Length = 12yards

W = L+2

W = 12+2

Width = 14yards

Sum of the length and width will be:

L+W= 12+14

= 26yards

Answer:

The length  of playground is 12 yd

The width of playground is 14 yd

The sum of the length and width of playground is 26 yd

Step-by-step explanation:

The area, A of the playground is given as 168 yd²

The formula for the area of the playground is given as follows;

Area, A of playground = Length, L × Width, W

The Width =  length  + 2 yd or W  = L + 2

Therefore, A = L × (L + 2)

A = L² + 2·L

Where we have A = 168 yd², we have the area equation presented as follows

168 = L² + 2·L or

L² + 2·L - 168 = 0

Factorizing the above equation gives

L = 12 or L = -14 we note that the appropriate solution is L = 12 yd

Therefore W = L + 2 = 12 + 2 = 14 yd

The length  of playground = 12 yd

The width of playground = 14 yd

The sum of the length and width of playground = 12 + 14 = 26 yd.

Answer:

1.6

Step-by-step explanation:

[tex] \tan \: A = \frac{4}{5} \\ \\ \cot \: A = \frac{1}{ \tan \: A } = \frac{1}{ \frac{4}{5} } = \frac{5}{4} \\ \\ csc\: A = \sqrt{1 + {cot}^{2}\: A} \\ = \sqrt{1 + { \bigg( \frac{5}{4} \bigg)}^{2} } \\ = \sqrt{1 + \frac{25}{16} } \\ = \sqrt{\frac{16 + 25}{16} } \\ = \sqrt{\frac{41}{16}} \\ = \frac{ \sqrt{41} }{4} \\ = \frac{6.40312424}{4} \\ = 1.60078106 \\ \therefore \: csc \: A =1.6[/tex]

Answer: radius = 3.61 cm

Step-by-step explanation:

The formula for determining the volume of a cylinder is expressed as

Volume = πr²h

Where

r represents the radius of the cylinder.

h represents the height of the cylinder.

π is a constant whose value is 3.14

From the information given,

Volume = 299 cm³

Height = 7.3 cm

Therefore,

299 = 3.14 × r² × 7.3

299 = 22.922r²

r² = 299/22.922 = 13.044

Taking square root of the left hand side and the right hand side of the equation, it becomes

r = 3.61 cm

Answer:

7 inches

Step-by-step explanation:

Height : Diameter

14 : 6

H : 3

H/14 = 3/6

H = 14 × 3/6

H = 7

Answer:

7 inches

Step-by-step explanation:

Answer: m<D = 80º

Step-by-step explanation:

Since we know triangle ABC is congruent to triangle EDC, the angle 60º can be know for angle ACB. Triangles have a interior total of 180, so 40+60 is 100. Subtract 100 from 180 to get your angle of B. Since the triangles are similar we know that B=D so D=80º

Answer:

Santiago earns 8.7 $ from each sold shirt

Step-by-step explanation:

1). 45 % of 6 is = 6 * 0.45 = 2.7 $

2). 6 $ + 45 % of 6 = 6 + 2.7 = 8.7 $ - Answer

Answer:

10

Step-by-step explanation:

You can use process of elimination for this question

Since one of the chord is drawn in and part on the radius is connected to it, that "part" radius bisects the chord

Therefore, the chord is 16 units long

Then the diameter must be even longer

The only option that works for the radius is 10 as the diameter would be 20

If the radius was 5, the diameter would be 10 which is less than the chord

If the radius was 6, the diameter would be 12 which is less than the chord