A prime die uses the first six prime numbers on its faces, one prime per face. When two prime dice are rolled randomly, there is a 1/36 probability that the product of the two numbers will be equal to 4. What is the probability that the product has a units digit of one

Answer:

B. 2

Step-by-step explanation:

on Edg2020

Answer:

B. 2 got it right

Step-by-step explanation:

Answer:

c.140

Step-by-step explanation:

Answer:

C. 140 degrees

Step-by-step explanation:

Answer:

Step-by-step explanation:

diameter = 8 units

r = 8/2 = 4 units

h = 6 units

[tex]Volume=\frac{1}{3}\pi r^{2}h\\\\=\frac{1}{3}*\pi*4*4*6\\\\[/tex]

= π*4*4*2

=32π cubic units

Answer: 15 yards

Step-by-step explanation:

From the question, we have been informed that the Steelers are on the Cowboys' fifteen-yard line. Using the place value mat to calculate how much farther Steelers need to travel to score a touchdown goes thus:

Since the play is 15 yards from the Cowboys end-zone, therefore Steelers need to travel 15 yards for them score a touchdown.

Final answer:

The Steelers are 85 yards away from the end zone.

Explanation:

To calculate how much farther the Steelers need to travel to score a touchdown, we need to know the distance from the Cowboys' fifteen-yard line to the end zone. The distance between each yard line on a football field is 10 yards. Since the Steelers are on the fifteen-yard line, they are 85 yards away from the end zone (100 yards - 15 yards = 85 yards).

The amount of flour alice had used at the end of the week is;

Amount = ¹/₂ pounds

Amount of flour she had at the start of the week = 3¹/₄ pounds

Amount she had at the end of the week = 2³/₄ pounds

Thus;

3¹/₄ pounds = 13/4 pounds

2³/₄ pounds = 11/4 pounds

Thus,

amount of flour she used = amount at the start of week - amount left at end of week

The denominator is the same and so our solution is to just subtract the numerator and retain the common denominator. This gives;

Amount of flour she used = ¹/₂ pounds

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Part A:

s = k + 4

Part B:

s = 13 + 4

s = 17

Therefore, Sylvia's age is 17 when Katie is 13.

The cube and rectangular prism.

Step-by-step explanation:

The triangular prism has 5 and the other two both have 8.

None of the shapes mentioned in the question, a cube, a rectangular prism, or a triangular prism, have more than six faces. For more complex shapes like Icosahedron, they do carry more than six faces.

The student's question is about understanding which among the shapes - a cube, a rectangular prism, and a triangular prism - has more than six faces. To answer this, we should first understand that a cube and a rectangular prism (or cuboid) both have 6 faces and a triangular prism also has 5 faces only. Hence, none of these shapes deliver more than 6 faces as specified in the question. For a three-dimensional shape to have more than 6 faces, one has to move towards more complex shapes. For example, the provided reference suggests Icosahedron, a shape with 20 faces is an example of a shape with more than six faces.

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Answer:

They will have $1651 after two years.

Step-by-step explanation:

The compound interest formula is given by:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.

$1500 dollars into an account at an annual rate of 4.8%

This means that [tex]P = 1500, r = 0.048[/tex]

Interest compounded twice a month.

A year has 12 months.

So 12*2 = 24 compundings, which means that [tex]n = 24[/tex]

How much will they have after two years?

This is A(2).

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]A(2) = 1500(1 + \frac{0.048}{24})^{24*2} = 1651[/tex]

They will have $1651 after two years.

Question:

You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% and​ 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If​ convenient, use technology to construct the confidence intervals. A random sample of 45 home theater systems has a mean price of ​$114.00. Assume the population standard deviation is ​$15.30. Construct a​ 90% confidence interval for the population mean.

Answer:

At the 90% confidence level, confidence interval = 110.2484 < μ < 117.7516

At the 95% confidence level, confidence interval = 109.53 < μ < 118.48

The 95% confidence interval is wider

Step-by-step explanation:

Here, we have

Sample size, n = 45

Sample mean, [tex]\bar x[/tex] = $114.00

Population standard deviation, σ = $15.30

The formula for Confidence Interval, CI is given by the following relation;

[tex]CI=\bar{x}\pm z\frac{\sigma}{\sqrt{n}}[/tex]

Where, z is found for the 90% confidence level as ±1.645

Plugging in the values, we have;

[tex]CI=114\pm 1.645 \times \frac{15.3}{\sqrt{45}}[/tex]

or CI: 110.2484 < μ < 117.7516

At 95% confidence level, we have our z value given as z = ±1.96

From which we have [tex]CI=114\pm 1.96 \times \frac{15.3}{\sqrt{45}}[/tex]

Hence CI: 109.53 < μ < 118.48

To find the wider interval, we subtract their minimum from the maximum as follows;

90% Confidence level: 117.7516 - 110.2484 = 7.5

95% Confidence level: 118.47503 - 109.5297 = 8.94

Therefore, the 95% confidence interval is wider.

Answer:

B. is the correct option.

With 90% the population mean price is

in lies in (127.01,134.99). With 95% confidence, it can be said that the population mean price lies in ( 126.24,135.76)

Therefore, the 95% confidence interval is wider than 90%.

The calculation is attached

Answer:

$47,000

Step-by-step explanation:

Let u represent the unknown amount of budget

10/100× u = $5000

10u/100=$5000

Cross multiply both sides

10u= $500000

Divide both sides by the coefficient of u

10u/10=$500000/10

u= $50000

Therefore, this year's budget is $50000

Since Smith's budget this year is $3000 greater than last year's budget, to find last year's budget we simply subtract the difference from this year's budget.

$50000- $3000

= $47000

Thus, Smith's total budget for last year was $47000.

Answer: $47,000

Step-by-step explanation:

Hi, to answer this question we have to write an equation:

Their total budget this year is $3,000 more than last year, so we have to add 3000 to their total budged of last year (x). x+3000

Since they spend 10% of their budget on entertainment, we have to multiply the previous expression by the percentage in decimal form (divided by 100).

(x +3000) 10/100 = (x+3000) 0.1

Finally, that expression must be equal to the amount that they will spend in entertainment this year (5000).

(x + 3000) 0.1 =5000

Solving for x:

x+3000 = 5000/0.1

x +3000= 50,000

x = 50,000-3,000

x = $47,000

Feel free to ask for more if needed or if you did not understand something.  

Answer:

[tex]2\frac{1}{12}[/tex] cups of sugar required for 5 cups of flour

Step-by-step explanation:

Number of cups of sugar required for 3 cups of flour =[tex]1 \frac{1}{4}[/tex]

Number of cups of sugar required for 3 cups of flour = [tex]\frac{5}{4}[/tex]

Number of cups of sugar required for 1 cup of flour [tex]=\frac{\frac{5}{4}}{3}[/tex]

Number of cups of sugar required for 5 cups of flour =[tex]\frac{\frac{5}{4}}{3} \times 5[/tex]

Number of cups of sugar required for 5 cups of flour =[tex]\frac{25}{12}[/tex]

Number of cups of sugar required for 5 cups of flour =[tex]2\frac{1}{12}[/tex]

Hence [tex]2\frac{1}{12}[/tex] cups of sugar required for 5 cups of flour

Answer:

C. 16

Step-by-step explanation:

12÷2×3−(7−5) = 16.

I hope this helps!

Following the order of operations (PEMDAS/BODMAS), the expression simplifies as:- 12 ÷ 2 * 3 - (7 - 5) = 6 * 3 - 2 = 18 - 2 = 16. So, the value is 16.

To find the value of the expression 12 ÷ 2 * 3 - (7 - 5), we need to follow the order of operations, often remembered using the acronym PEMDAS (or BODMAS):

1. Parentheses (or Brackets): First, we evaluate what's inside the parentheses. In this case, (7 - 5) equals 2.

2. Exponents (or Orders): There are no exponents or orders in this expression.

3. Multiplication and Division: After dealing with parentheses, we move from left to right. So, 12 ÷ 2 * 3 is calculated as follows:

  12 ÷ 2 * 3 = 6 * 3 = 18

4. Addition and Subtraction: Again, we move from left to right. Now we subtract 2 (the result from step 1) from 18 (the result from step 3):

  18 - 2 = 16

So, the final answer is 16.

In summary, using the order of operations, the expression simplifies to 16. It's crucial to follow these rules to ensure that mathematical expressions are evaluated correctly, as different orders can lead to different results.

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Answer:

B is your answer

Step-by-step explanation:

Final answer:

The correct comparison is that 4.06 is less than 4.6 because when looking at the decimal parts, '0.6' (4.6) is greater than '0.06' (4.06).

Explanation:

To compare the numbers 4.06 and 4.6, we need to look at the decimal parts, since the whole number part (4) is the same for both. In the number 4.06, the decimal part is '06', which is actually '0.06' when read as a fraction of the whole number. On the other hand, 4.6 has a decimal part of '6', which is '0.6' as a fraction of the whole number. When comparing '0.6' and '0.06', it is clear that '0.6' is larger because '6' tenths is greater than '6' hundredths.

Therefore, the correct comparison between 4.06 and 4.6 is 4.06 < 4.6, which corresponds to option D in the question.

Answer:

[tex]\frac{x}{3}[/tex]+4

Step-by-step explanation:

I don't think it can be simplified more than that

Answer:

x= -12

Step-by-step explanation:

x/3 -2+6 =0

x/3 +4 =0

x/3 = -4

x/3 (3) = -4 (3)

x = -12

Answer:

d) none of the above

Step-by-step explanation:

correct me if wrong .

Final answer:

The equation tan^2(x) + 3 = 0 has no real solutions within the given range.

Explanation:

To solve the equation tan^2(x) + 3 = 0, we need to isolate the term with the tangent squared. Subtracting 3 from both sides gives us tan^2(x) = -3. Since the tangent function is positive for angles between 0° and 360°, it is not possible for the square of the tangent to be negative. Therefore, there are no real solutions to this equation, given the specified range of 0 ≦ x < 360°. So, the correct answer is (D) None of the above.

Answer:

The vertex of the function is at (–3,–16)

The graph is increasing on the interval x > –3

The graph is positive only on the intervals where x < –7 and where x > 1

Step-by-step explanation:

The roots of this function are the values that make f(x) = 0. As the equation is already factored, we can see that the roots are x1 = 1 and x2 = -7

The x-coordinate of the vertix can be calculated as:

x_v = (x1 + x2)/2 = -6/2 = -3

So the first statement: "The vertex of the function is at (–4,–15)" is wrong.

The y_coordinate of the vertex is:

f(x_v) = (x_v - 1)*(x_v + 7) = (-3 -1) * (-3 +7) = (-4) * (4) = -16

So the second statemente: "The vertex of the function is at (–3,–16)" is correct.

for values of x greater than x_v = -3, the graph increases, as the equation represents a parabola with concavity upwards. So the third statement is correct.

As the roots are 1 and -7 and the concavity is upwards, the parabola have positive values for x<-7 and x>1. So the fourth statement is correct.

For values of x< -4, the parabola can have both positive or negative values (it has positive values for x < -7) so the fifth statement is wrong.

Answer:

B. The vertex of the function is at (–3,–16).

C. The graph is increasing on the interval x > –3.

D. The graph is positive only on the intervals where x < –7 and where

x > 1.

Answer: the computer loses 50% of its value each year

Step-by-step explanation:

Look at the attached picture

Hope it will help you...

Good luck on your assignment

~pragya

Answer:

32.5

Step-by-step explanation:

its a trick question

Answer:

x

Step-by-step explanation:

We are required to simplify the rational expression:

[tex]\dfrac{4}{x^2+4x-5} -\dfrac{5}{x^2-25}[/tex]

First, we factorize the denominators where possible

[tex]x^2+4x-5=x^2+5x-x-5=x(x+5)-1(x+5)=(x-1)(x+5)\\x^2-25=x^2-5^2 \\$Applying difference of two squares\\x^2-5^2=(x-5)(x+5)[/tex]

Therefore, our rational expression becomes:

[tex]\dfrac{4}{(x-1)(x+5)} -\dfrac{5}{(x-5)(x+5)}\\$Taking LCM\\=\dfrac{4(x-5)-5(x-1)}{(x-1)(x-5)(x+5)}\\=\dfrac{4x-20-5x+5}{(x-1)(x-5)(x+5)}\\=\dfrac{-x-15}{(x-1)(x-5)(x+5)}\\$Factoring out minus in the numerator and -(x-5)=(5-x)\ in the denominator\\=\dfrac{x+15}{(x-1)(5-x)(x+5)}[/tex]

Therefore, the leading coefficient of the numerator is x.

Answer: 54 miles per hour

Step-by-step explanation:

Max travles to see his brother 's family by car and he drives 216 miles in 4 hours. To calculate his rate in miles per hour, we divide the amount of distance he travelled by the number of hours used. This will be:

Distance= 216 miles

Time taken= 4 hours

Speed = Distance travelled/Time taken

= 216/4

= 54 miles per hour

Answer:

The first picture is A

The second picture is 21.8

The third picture is 20

The fourth picture is B

Step-by-step explanation:

4x + 8x = 180

12x = 180

x = 15

90 - 68.2 = 21.8

7x + 10 = 150

7x = 140

x = 20

Angle A = 63

180 - 63 = 117

Answer:

The first picture is A

The second picture is 21.8

The third picture is 20

The fourth picture is B

Step-by-step explanation:

hope this helps

Answer:

10.95

Step-by-step explanation:

anything under 4 rounds down and anything over 4 rounds up. so your answer would be 10.95

10.9544 rounded to the nearest tenth would be 11.0. When rounding to the nearest anything, remember to look at the number to the right of it. If it is greater or equal to five, round up. If the number is less than five, round down. In this situation, the number to the right of "9" (the position of the tenth) is five, which means we should round up, which would equal 11.

I hope this helped -- if it did, please thank, rate, and mark as brainliest! If you have any more questions or concerns, feel free to ask! Thank you, stay safe, and have a great rest of your day/quarantine! (i know it's hard, but we're almost through. we've got it!)

Answer:

1.5cm³

Step-by-step explanation:

Surface area of a prism = bh x 6

0.5 x 0.5 = 0.25 x 6 = 1.5

Answer:

1.5 cm

Step-by-step explanation:

a=6a^2

a=6(0.5)^2

a=6(0.25)

a=1.5 cm

Answer:

The answer is c I think

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

I took test and got 100%

Answer:

x = ±8

Step-by-step explanation:

X^2- 64

Set this equal to 0

x^2 -64 =0

Add 64 to each side

x^2-64+64 = 64+64

x^2 = 64

Take the square root on each side

x = ±sqrt(64)

x = ±8

Answer:

Step-by-step explanation:

a²-b²=(a+b)(a-b)

x²-64=x²-8²

=(x+8)(x-8)

Answer:

1. 3x + 2  - First degree

2. 4x3 + 17x - 5  - Third degree

3. 13x" + 5xn-2  - Second degree

4. 0.55x2 + 0.7x  - Second degree

5. 7x3 + 10x + 15  - Third degree

Step-by-step explanation:

The degree of a polynomial is given by the highest power of the given variable (x in this case) in the polynomial. All the elements are considered in selecting the highest power of x in the polynomials.

Considering all; the highest degree of x in the polynomials given is 3 while the lowest is 1 hence we have polynomials ranging from the first to third degrees.

Answer:

(0,1)

Step-by-step explanation:

Any real number to the power of 0, including 6, is equal to 1. Therefore, f(0) is 1, and the y intercept is (0,1). Hope this helps!