g) A small rectangular block of fudge has dimensions: 1,5 cmx1,5 cmx3 cm. Blocks of fudge must be put into a large rectangular box with a capacity of 162 m/. Calculate the volume of a block of fudge. How many blocks of fudge can be put into the large rectangular box? (3) If the length of a block of fudge is 3 cm and the breadth (B) of the large box is 3 cm, determine the length (L) and height (H) of the box. (1) (2) HL B 3 cm The obte orga Dis Co A​

Answer:

a

The 95% confidence interval is \(1003 < \mu <1023\)

b

Yes there is statistically significant evidence that students in Florida perform differently from other students in the United States

Step-by-step explanation:

From the question we are told that

   The population mean is  \(\mu = 1000\)

   The sample size is  \(n = 453\)

   The sample mean is  \(\= x = 1013\)

    The standard deviation is \(s = 108\)

Given that the confidence level is  95% then the level of significance is mathematically represented as

            \(\alpha = 100 - 95\)

=>         \(\alpha = 5\%\)

=>          \(\alpha = 0.05\)

The critical value  for \(\frac{\alpha }{2}\) obtained from the normal distribution table is          

          \(Z_{\frac{\alpha }{2} } = 1.96\)

Generally the margin of error is mathematically represented as

         \(E = Z_{\frac{\alpha }{2} } * \frac{s}{\sqrt{n} }\)

=>     \(E = 1.96 * \frac{108}{\sqrt{453} }\)

=>      \(E = 9.946\)

Generally the 95% confidence interval is mathematically represented as

           \(\= x - E < \mu < \= x + E\)

=>         \(1013 - 9.946 < \mu < 1013 + 9.946\)

=>         \(1003 < \mu <1023\)

Given that the population mean(1000) is not within the 95% confidence interval for l for the average test score for students in Florida, then it means that there is statistically significant evidence that students in Florida perform differently from other students in the United States

The system of equations has only one solution and is the point (1, 1)

Here we have the graph of a system of equations, where we can see that both of them are linear equations.

Whenw e have a graph of a system, the solutions are all the points where the graphs of the equations intercept.

On the given graph, we can see that the two lines intersept at the point (1, 1)

So we have only one solution and is the point (1, 1)

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Answer:

Vertex: (-4, 1)

X intercepts: (-6, 0) and (-2, 0)

Y Intercepts: (0, -5)

Axis of Symmetry: X= -4

Step-by-step explanation:

Vertex of the parabola is the maximum or minimum point on the graph of the quadratic function

X intercepts are points of when a line or in this case a parabola intercepts the x axis, and where y = 0

Y intercepts are point of when a line or in this case a parabola intercepts the y axis, and where y = 0

Axis of symmetry is the point where if you divide the parabola in half, shows a symmetrical side

Answer:

\([7\times(-2)]^5 = 7^5 \times (-2)^5\)

Step-by-step explanation:

Answer:

2(4x-3) + 6(3y-5)

X=5 and y=7

2(4(5)-3) + 6(3(7)-5)

2(20-3) + 6(21-5)

2(17) + 6(16)

34 + 96

130

Step-by-step explanation:

The volume of the canister is 36.7 in³. The volume of box is 482.6 cm³

To find the volume of a canister, we can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

In this case, the canister has a radius of 1.56 inches and a height of 6.93 inches,

volume of canister = π × (1.56 inches)² × 6.93 inches

volume of canister = 36.7 in³

To find the volume of a box, we can use the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height.

In this case, the box has a length of 15.5 cm, a width of 8.6 cm, and a height of 3.8 cm

volume of box = 15.5 cm × 8.6 cm × 3.8 cm

volume of box = 482.6 cm³

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The joint costs allocated to Product B is $240,000.

We must allocate joint costs based on the relative physical quantities produced by each product.

The total physical quantity produced by both products is:

= Quantity of A + Quantity of B

= 10,000 + 40,000

= 50,000 pounds

We will calculate the proportion of physical quantity produced by product A:

= Quantity of B / Total physical quantity

= 40,000 / 50,000

= 0.8

The amount of joint costs allocated to Product B is will be

= Total joint costs x Proportion of

= $300,000 x 0.8

= $240,000.

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Answer:

D. 3 points purchased

Step-by-step explanation:

Took the bullet

Option D is correct, based on the information Gordon purchased 3 point

A fraction represents a part of a whole.

Given that Gordon decided on purchasing a $141,000 home.

At closing he brought a check for $7570.

One point is equal to 3% of the total loan amount, so the cost of one point would be:

Cost of one point = 3% of $130,090

Cost of one point = $3,902.70

To find out how many points Gordon purchased

we need to divide the total cost of points by the cost of one point:

Number of points = Total cost of points / Cost of one point

Number of points = $10,910 / $3,902.70

Number of points = 2.8

=3

Therefore, based on the information Gordon purchased 3 points, Option D is correct.

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Answer:

I Think its 81.68141

Here are the correct matches to the expressions to their solutions.

The GCF of 28 and 60 is 4.

(-3/8)+(-5/8) = -4/4 = -1.

-1/6 DIVIDED BY 1/2 = -1/6 X 2 = -1/3.

The solution of 0.5 x = -1 is x = -2.

The solution of 1/2 m = 0 is m = 0.

-4 + 5/3 = -11/3.

-2 1/3 - 4 2/3 = -10/3.

4 is not a solution of -4 < x.

1. The GCF of 28 and 60 is 4.

The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 28 and 60, we can factor each number completely:

28 = 2 x 2 x 7

60 = 2 x 2 x 3 x 5

The factors that are common to both numbers are 2 and 2. The GCF of 28 and 60 is 2 x 2 = 4.

2. (-3/8)+(-5/8) = -1.

To add two fractions, we need to have a common denominator. The common denominator of 8/8 and 5/8 is 8. So, (-3/8)+(-5/8) = (-3 + (-5))/8 = -8/8 = -1.

3. -1/6 DIVIDED BY 1/2 = -1/3.

To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/2 is 2/1. So, -1/6 DIVIDED BY 1/2 = -1/6 x 2/1 = -2/6 = -1/3.

4. The solution of 0.5 x = -1 is x = -2.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate x by dividing both sides of the equation by 0.5. This gives us x = -1 / 0.5 = -2.

5. The solution of 1 m = 0 is m = 0.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate m by dividing both sides of the equation by 1. This gives us m = 0 / 1 = 0.

6. -4 + 5/3 = -11/3.

To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction. In this case, we can convert -4 to -4/3. So, -4 + 5/3 = -4/3 + 5/3 = -11/3.

7. -2 1/3 - 4 2/3 = -10/3.

To subtract two fractions, we need to have a common denominator. The common denominator of 1/3 and 2/3 is 3. So, -2 1/3 - 4 2/3 = (-2 + (-4))/3 = -6/3 = -10/3.

8. 4 is not a solution of -4 < x.

The inequality -4 < x means that x must be greater than -4. The number 4 is not greater than -4, so it is not a solution of the inequality.

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If a rectangular prism has a length of 2 meters, a width of 4 meters, and a height of 2 meters. The volume of the prism is 16 cubic meters.

The volume of a rectangular prism is given by the formula:

Volume = length x width x height

Substituting the given values, we get:

Volume = 2 meters x 4 meters x 2 meters

Simplifying this expression, we get:

Volume = 16 cubic meters

Therefore, the volume of the prism is 16 cubic meters.

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Answer:

A. 3x+12

Step-by-step explanation:

8x+3-5x+9

8x-5x=3x

3+9=12

then put them together

3x+12

answer= A

We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot.

A statistical test is required to determine whether the length of the left foot is greater than the length of the right foot. The null hypothesis states that there is no difference in average length between the left and right feet. The alternative hypothesis is that the left foot's average length is greater than the right foot's average length.

This hypothesis is one-tailed, as we are only interested in whether the left foot is longer than the right foot. We are not considering the possibility that the right foot could be longer than the left foot.

A t-test can be used to determine whether the difference in average length between the left and right feet is statistically significant. We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot if the p-value of the t-test is less than the chosen significance level (e.g., 0.05).

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Answer:

15. 4x¹⁰

16. 30m³

Step-by-step explanation:

15. Area of Rectangle is given by A=LW

    since W=x⁵ and L is 4 times W, L=4x⁵

    therefore, A = x⁵(4x⁵) = 4x¹⁰

16. Volume of Rectangular Prism is V=LWH

    W=6L=6m  and  H=5L=5m  and  L=m

   so V = m(6m)(5m) = 30m³

Answer:100

Step-by-step explanation:

40+40 =80 +20=100

Answer:

c is the right answer

Answer:

A

Step-by-step explanation:

I say a because it's supposed to bring the Venn diagram alone

Answer:

\(\red{ \bold{ 7 {x}^{2} + 180x + 324 = 0}}\)

Step-by-step explanation:

Given is an isosceles right triangle.

Therefore, by Pythagoras theorem:

\( {(5x + 18)}^{2} = {( - 3x)}^{2} + {( - 3x)}^{2} \\ \\ \implies \: {(5x)}^{2} + 2(5x)(18) + {(18)}^{2} = 9 {x}^{2} + 9 {x}^{2} \\ \\ \implies \: 25 {x}^{2} + 180x + 324 = 18 {x}^{2} \\ \\ \implies \: 25 {x}^{2} - 18 {x}^{2} + 180x + 324 = 0 \\ \\ \implies \: \ \red{ \bold{ 7 {x}^{2} + 180x + 324 = 0}}\\ \\ \)

if other experts state the same thing in their own paper or document.

Answer:

a

Step-by-step explanation:

expressions dont have answers

So, the two balls are located on the same plane, the x-y plane, with the baseball at <3,5,0>m and the tennis ball at <-3,-1,0>m, with the vector pointing from baseball to the tennis ball is <-6,-6,0>m.

The position vector of the baseball is <3,5,0>m. The position vector of the tennis ball is <-3,-1,0>m.

The position vector of the tennis ball relative to the baseball is the vector pointing from the baseball to the tennis ball and it is calculated by subtracting the position vector of the baseball from the position vector of the tennis ball: <-3,-1,0>m - <3,5,0>m = <-6,-6,0>m

So the two balls are located on the same plane, the x-y plane, with the baseball at <3,5,0>m and the tennis ball at <-3,-1,0>m, with the vector pointing from baseball to the tennis ball is <-6,-6,0>m.

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Answer:

51.639-38.709

18.63-5.7

Step-by-step explanation:

Hope it helps...

Answer:

area = 1/2*b*h

h^2=hypotenuse^2-base^2

h^2= 2^2-1^2

h^2=4-1

h^2=3

h=√3

1/2*2*√3

=√3

Answer:

2/9

Step-by-step explanation:

each city has a probability of 1/9

one city 'or' another means to add their probabilities:  1/9 + 1/9 = 2/9

The probability of Cleveland or Dallas getting picked is \(\frac{2}{9}\).

'Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.'

According to the given problem,

Total number of city names = 9

Favorable events = 2 [ Cleveland, Dallas]

Probability = \(\frac{Favorable events}{Total number of events}\)

Probability of Cleveland getting picked = \(\frac{1}{9}\)

Probability of Dallas getting picked = \(\frac{1}{9}\)

Probability of Cleveland OR Dallas getting picked = \(\frac{1}{9}+\frac{1}{9}\)

                                                                                   = \(\frac{2}{9}\)

Hence, we can conclude, probability of Cleveland or Dallas getting picked is \(\frac{2}{9}\).

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Answer:

Step-by-step explanation:

(-1,7), (0,5), (1,3)

and

(0,-3), (2,5), (4,13)

Option (C)

Given:

Two segments are interesting outside the circle.

The objective is to find the correct equation.

Since the two lines drawn from a point outside the circle passes through two points in a circle, the line is call secant line.

Consider the given figure as,

If two secant line is drawn from a point outside the circle, the equation wil be,

Now, substitute the given values in the above formula,

Hence, option (C) is the correct answer.

Answer:

5:1

Step-by-step explanation:

d_a = 20

d_b = 5

Equation for the circumference of a circle:

C = pi*d

C_a = pi * d_a

C_a = pi*20

C_b = pi * d_b

C_b = pi * 5

Ratio of C_a to C_b = C_a/C_b

C_a/C_b = (pi * 20)/(pi * 4) = 5:1

Answer:

After finding the money we were short with, we find that Option-b, that is, $2200 is the correct option.

Step-by-step explanation:

Given that the cost to repair the damaged car is $2700. We have $500.

Insurance company is a company that gives the payment of someone's valuable items when they are lost or get damaged. For example, home insurance, car insurance, life insurance and much more.

Here we can see that we are short with $2700 - $500 = $2200.

So, to complete the payment, insurance company will pay $2200.

Clearly, the correct option is Option-b.

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The correct option regarding the number of bags filled by Nina, using proportions, is given as follows:

Between 20 and 30 bags.

A proportion is a fraction of an amount, and this fraction is combined with the unit rates of the problem and basic arithmetic operations, especially multiplication and division, to find the desired amounts in the context of the problem.

In this problem, a proportion is applied to find the number of bags filled by Nina, which is given by the division presented as follows:

Number of bags = Number of treats / Treats per bag.

The values of these parameters are given as follows:

Hence the numeric value of the expression is:

Number of bags = 78/3 = 26.

Which is a number between 20 and 30.

The problem states that Nina had 78 treats, and each bag has 3 treats, then it asks the correct option regarding the number of bags.

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Answer:

(x) ∠CAB

Step-by-step explanation:

In ΔCOD and ΔBOA

\(\frac{OA}{OB} = \frac{OD}{OC} \\\\\implies \frac{OC}{OB} = \frac{OD}{OA}\)

Also,

∠COD = ∠BOA (vertically opposite angles)

⇒ ΔCOD and ΔBOA are similar

⇒ ∠CDO = ∠BAO

⇒ ∠CDB = ∠BAC

⇒ ∠CDB = ∠CAB

The correct answer is $131250

Explanation:

Talia's earnings during one year are equal to her base yearly salary ($65000) added to her commission. Now, to know the commission it is necessary to find the 2.65% of her total sales ($2.5 million)

1. Divide the total sales or 2,500,000 by 100 considering this represents the total or 100%

2,500,000 ÷ 100 = 25000

2. Multiply this number by the specific percentage (2.65)

25000 x 2.65 = 66250

Now add the commission and the yearly salary

65000 + 66250 = 131250

This means the total earnings of Talia were $131250

2.65% = 0.0265

0.0265 x 2,500,000 = 66250

66250 + 65000 = 131,250