A company sells cardboard scratching blocks for cats. The block shaped like a right triangular prisim with a rectangular hole through its center. What is the total area of the blocks scratching surface.

Answer:

He took 3 3/4 hours to clean both rooms.

Step-by-step explanation:

1/2 = 2/4

3 1/4 + 2/4 = 3 3/4

Therefore, he took 3 3/4 hours.

The statement  that is true about standard deviation is

Option D is the correct answer.

We have,

Standard deviation is a measure of how spread out the data is in a set.

A smaller standard deviation indicates that the data points are closer to the mean, while a larger standard deviation indicates that the data points are more spread out from the mean.

Since the standard deviation of set A is 6 and the standard deviation of set B is 9, we can conclude that the data in set A varies less than the data in set B.

So,

The data in set A varies less than the data in set B.

Thus,

The statement  that is true about standard deviation is

The data in set A varies less than the data in set B.

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The statement  that is true about standard deviation is

Option D is the correct answer.

We have,

Standard deviation is a measure of how spread out the data is in a set.

A smaller standard deviation indicates that the data points are closer to the mean, while a larger standard deviation indicates that the data points are more spread out from the mean.

Since the standard deviation of set A is 6 and the standard deviation of set B is 9, we can conclude that the data in set A varies less than the data in set B.

So,

The data in set A varies less than the data in set B.

Thus,

The statement  that is true about standard deviation is

The data in set A varies less than the data in set B.

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Answer:

The correct answer is D. 5.4% after rounding my answer off to the nearest tenth of a percent.

When the simultaneous equation is solved, we have that;  x = 2 and y = 3

Simultaneous equations are a set of two or more equations that are solved together to find the values of the variables that satisfy all of the equations at the same time.

We have the equations;

9x - 7y = -3 --- (1)

-3x + 5y = 9 ---- (2)

Multiply (1) by 1 and (2) by (3)

9x - 7y = -3  ---- (3)

-9x + 15y = 27 ----- (4)

Add (3) and (4)

8y = 24

y = 3

Substitute y = 3 into (1)

9x - 7(3) = -3

9x - 21 = -3

9x = -3 + 21

9x = 18

x = 2

Thus the solution is x = 2 and y = 3

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Answer:

c. 8 2/8

Step-by-step explanation:

12 1/2 - 4 7/10 = 12 5/10 - 4 7/10 = 8 2/10 = 8 1/5 = 8.2

Therefore, the answer is option c. 8 2/8

Hope this helps!

Answer:

Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).

1 + 2cos a = 2(cos a/2 + 1)

Step-by-step explanation:

We can use the trigonometric identity:

cos 2a = 1 - 2 sin^2 a

to rewrite 1 + 2cos a as:

1 + 2cos a = 1 + 2(1 - sin^2 a/2)

= 1 + 2 - 2(sin^2 a/2)

= 3 - 2(sin^2 a/2)

Now, using another trigonometric identity:

sin a = 2 sin(a/2) cos(a/2)

we can rewrite sin^2 a/2 as:

sin^2 a/2 = (1 - cos a)/2

Substituting this into the expression for 1 + 2cos a, we get:

1 + 2cos a = 3 - 2((1 - cos a)/2)

= 3 - (1 - cos a)

= 2 + cos a

Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).

1 + 2cos a = 2(cos a/2 + 1)

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by

[tex]\text{Z}=\dfrac{\text{X}-\mu}{\sigma}[/tex]

After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X.

In this problem, we have that:

A study conducted in 2012 found the length of Atlantic cod caught in nets in Karlskrona to have a mean of 49.9 cm and a standard deviation of 3.74 cm, so [tex]\mu=49.9,\sigma=3.74[/tex].

What is the length in cm of the longest 15% of Atlantic cod in this area?

We have to find the value of X for the value of Z that has a p-value of 0.85.

Looking at the z-score table, we have that Z = 1.04 has a p-value of 0.8508. So, we have to find the value of X when .

So

[tex]\text{Z}=\dfrac{\text{X}-\mu}{\sigma}[/tex]

[tex]1.04=\dfrac{\text{X}-49.9}{3.74}[/tex]

[tex]\text{X}-49.9=3.8896[/tex]

[tex]\text{X}=53.7896[/tex]

The length of the longest 15% of Atlantic cod in this area is 53.79 cm, rounded to 2 decimal places.

Answer:

Step-by-step explanation:

Use a simple Equation

Price = Number x Price

So Price = 536.

Since it was 67% off we multiple the price of the original by .67.

So

536 = .67x

Solve for x = 536/.67 = 800

The original Price is $800.

check by multiplying by the sale %.

Answer :

Answer : 1.796

The explanation is in the pictures.

Answer:

percentage increase: 43,75%

Step-by-step explanation:

If we want to solve thai as an equation, we can write:

800 + (x/100) * 800 = 1150

we multiply: 800 + 800x/100 = 1150

we simplify: 800+ 8x = 1150

we bring the unknown to the left, and numbers to the right:

8x = 1150 - 800

8x = 350

we find x by dividing each part by 8

x= 43,75

(note that the x/100 in the first equation is the same thing as writing x%, so 800 plus a percentage of 800 is equal to 1150)

The area and circumference of a circle with diameter of 3 m is 7.0165 m² and 9.42 m² respectively

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The area of a figure is the amount of space it occupies in its two dimensional state.

The diameter (d) of the circle is 3 meter. Hence:

Area = π * diameter²/4 = π * 3²/4 = 7.0165 m²

Circumference = π * diameter = π * 4 = 9.42 m²

The area and circumference are 7.0165 m² and 9.42 m²

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Answer:

7,920

Step-by-step explanation:

I took test and got 100%

We can see here that the triangle is a right-angle triangle.

The fundamental geometric shape of a triangle has three straight sides and three angles. It is a triangular polygon with three edges.

We can see here that the triangle is a right-angle triangle because using Pythagoras Theorem, we will see the following:

Hypotenuse = c = 30

Adjacent = b = 24

Opposite = a = 18

c² = a² + b²

Hyp² = Opp² + Adj²

30² = 18² + 24²

324 + 576 = 900.

Thus, it is a right-angle triangle.

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The range of function for the given domain are {25, 8, -7, 11}

Given that, a function f(x) = 2x²-7, we need to find the range of the function, for the given domain, x = {-4, -2, 0, 3},

So,

Domain = All the input values.

Range = All the output values.

So, to find the range we will put the value of x which is the domain and the value obtained of f(x) will be the range,

f(x) = 2x²-7

For, x = -4,

f(-4) = 16×2 - 7 = 25

f(-4) = 25

f(-2) = 4 × 2 - 7 = 8

f(-2) = 8

f(0) = -7

f(3) = 9 × 2 - 7

f(3) = 11

Hence the range of function for the given domain are {25, 8, -7, 11}

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The equation is 2m + 4s = 16 and the table of values is solved

Given data ,

Let the equation be represented as A

Now , the value of A is

2m + 4s = 16

when m = 0

4s = 16

s = 4

when s = 3

2m + 12 = 16

2m = 4

m = 2

when m = -2

-4 + 4s = 16

4s = 20

s = 5

when s = 0

2m = 16

m = 8

Therefore , the table of values for m = { 0 , 2 , -2 , 8 } and the table of values for s = { 4 , 3 , 5 , 0 }

Hence , the equation is solved

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We can deduce that option A is likely to be true based on the given graph of rolling dice median data.

The median is the value in the middle of a data set, which means that 50% of the data points have a value less than or equal to the median, and 50% of the data points have a value greater than or equal to the median.

The graph illustrates that the median value of the rolls is closer to the center of the possible outcomes (numbers 3, 4, and 5) than the extremes (numbers 1 and 6).

This implies that when rolling a dice several times, the median is less likely to fall between the numbers 1 and 6.

However, because rolling the dice is a random process, there is always a degree of uncertainty in predicting the outcomes.

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So the person would save approximately 244 yards by walking diagonally across the field instead of walking the length and width of the field separately.

what is  approximately  ?

"Approximately" is a word that is used to indicate that a value, quantity, or measurement is close to the actual or precise value, but not exactly the same. It means that the stated value is an estimate or approximation, and may be slightly different from the true value.

In the given question,

Using the Pythagorean theorem, we can find the length of the diagonal of the soccer field:

diagonal² = length² + width²

diagonal² = 110² + 80²

diagonal² = 12,100 + 6,400

diagonal² = 18,500

diagonal = √18,500

diagonal ≈ 136 yards

So the person walking diagonally across the field would cover a distance of approximately 136 yards.

To compare this with the distance they would cover if they walked the length and width of the field separately, we can use the formula for the perimeter of a rectangle:

perimeter = 2(length + width)

perimeter = 2(110 + 80)

perimeter = 2(190)

perimeter = 380 yards

Therefore, if the person walked the length and width of the field separately, they would cover a total distance of 380 yards.

The difference between these two distances is:

380 - 136 = 244 yards

So the person would save approximately 244 yards by walking diagonally across the field instead of walking the length and width of the field separately.

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So the person would save approximately 244 yards by walking diagonally across the field instead of walking the length and width of the field separately.

what is  approximately  ?

"Approximately" is a word that is used to indicate that a value, quantity, or measurement is close to the actual or precise value, but not exactly the same. It means that the stated value is an estimate or approximation, and may be slightly different from the true value.

In the given question,

Using the Pythagorean theorem, we can find the length of the diagonal of the soccer field:

diagonal² = length² + width²

diagonal² = 110² + 80²

diagonal² = 12,100 + 6,400

diagonal² = 18,500

diagonal = √18,500

diagonal ≈ 136 yards

So the person walking diagonally across the field would cover a distance of approximately 136 yards.

To compare this with the distance they would cover if they walked the length and width of the field separately, we can use the formula for the perimeter of a rectangle:

perimeter = 2(length + width)

perimeter = 2(110 + 80)

perimeter = 2(190)

perimeter = 380 yards

Therefore, if the person walked the length and width of the field separately, they would cover a total distance of 380 yards.

The difference between these two distances is:

380 - 136 = 244 yards

So the person would save approximately 244 yards by walking diagonally across the field instead of walking the length and width of the field separately.

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Step-by-step explanation:

the perimeter (the way one time around it) of a rectangle is

2×length + 2×width

length = 3×width

2×(3×width) + 2×width = 160

6×width + 2×width = 160

8×width = 160

width = 160/8 = 20 ft

length = 3×width = 3×20 = 60ft

Answer:

554.76 miles per hour

Step-by-step explanation:

[tex]\frac{248 meters}{1 second}[/tex] x [tex]\frac{3600 seconds}{1 hour}[/tex] x [tex]\frac{1 mile}{1609.34 meters}[/tex]

= 554.76 miles per hour

[tex]\sf 554.76(mi/h).[/tex]

[tex]\sf \dfrac{248(m)}{s}[/tex]

a) First, convert the meters to kilometers.

[tex]\sf 248(m)*\dfrac{1(km)}{1000(m)} =0.248(km)[/tex]

Here, the meters cancel, since one is on the numerator and the other one is expressed as a denominator, and we simpyl multiply the value by the fraction, resulting in a number that would be a value for kilometers.

b) Convert from kilometers to miles.

[tex]\sf 0.248(km)*\dfrac{1(mi)}{1.60934(km)} =0.1541(mi)[/tex]

[tex]\sf 1(seconds)*\dfrac{1(hour)}{3600(seconds)} =\frac{1}{3600}(h)[/tex]

[tex]\sf \dfrac{0.1541(mi)}{\dfrac{1}{3600} (h)} =554.76(mi/h)[/tex]

The graph of your equation is a parabola with x-intercepts at x = -8.75 and x = 7.25.

x = -8.75; x = 7.25

2(x + ¾)² - 5 = 123

Add 5 to each side:                     2(x+ ¾)² = 128

Divide each side by 2:                   (x+ ¾)² = 64

Take the square root of each side: x + ¾ = 8       x + ¾ = -8

Subtract ¾ from each side:                     x = 8 - ¾        x = -8 - ¾

Convert to decimal fraction:                    x = 8 - 0.75    x = -8 – 0.75  

Subtract:                                                   x = 7.25           x = -8.75

The graph of your equation is a parabola with x-intercepts at x = -8.75 and x = 7.25.

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The graph of your equation is a parabola with x-intercepts at x = -8.75 and x = 7.25.

x = -8.75; x = 7.25

2(x + ¾)² - 5 = 123

Add 5 to each side:                     2(x+ ¾)² = 128

Divide each side by 2:                   (x+ ¾)² = 64

Take the square root of each side: x + ¾ = 8       x + ¾ = -8

Subtract ¾ from each side:                     x = 8 - ¾        x = -8 - ¾

Convert to decimal fraction:                    x = 8 - 0.75    x = -8 – 0.75  

Subtract:                                                   x = 7.25           x = -8.75

The graph of your equation is a parabola with x-intercepts at x = -8.75 and x = 7.25.

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The confidence interval is given as (38.811,43.829)

In statistics, a margin of error refers to the degree of imprecision that can be projected in survey or polling outcomes due to random sampling involved in such studies.

This indicator serves as both the measure for the accuracy of results and an assurance of confidence in them. The percentage rate expressing the magnitude of the latter varies inversely with the former and depends on the sample size, desired level of confidence, and cumulative trends in feedback obtained from respondents.

Thus, surveys featuring minimal margins of error are considered substantively accurate while ones plagued by larger margins signal a lack thereof.

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The statements that are true about the scatter plot graph are;
1. The line of best fit should have the same number of points above and below it.

2. There is a moderate positive correlation.

3. The line of best fit will have a positive slope.

Some facts about scatter plot graphs:

Scatter plots are used to show the correlation or relationship between two variables. The variables are plotted on the x and y-axes, and each point represents a pair of values for the two variables.

Scatter plots can show different types of relationships between two variables, including positive, negative, or no correlation.

The shape of a scatter plot can provide insights into the strength and direction of the relationship between the two variables. For example, if the points on the scatter plot form a linear pattern, this indicates a strong correlation.

Scatter plots can be used to identify outliers or anomalies in the data that do not fit the general pattern of the relationship between the two variables.

The above answer is based on the following options provided in the picture.

Tick all the statements that applies

The y intercept of the line  of best fit would be around 45

The line of best fit should have the same number of points above and below it

The slope of the line of best fit could be around -1/20000

The line of best fit must pass through at lest 2 points on the scattered plot

There is no correlation between happiness and income

There is a moderate positive correlation

The line of best fit will have a positive slope

As a person's income goes up, their happiness trends down

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The adjascent angles to angle EDC is angle EDI and CDH.

Two angles are said to be adjacent angles when they share the common vertex and side. The sum of adjascent angles is 180°. This means that adding two adjascent angles together will give 180°. Adjascent angles are also called supplementary angles.

Examples of adjascent angles in the diagram include;

AEB Is adjascent to AED

and also there are two angles that are adjascent to angle EDC. They are;

angle ED1 and CDH

Therefore the adjascent angles to angle EDC is angle EDI and CDH.

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The graph that shows the image of ABC after a rotation about the origin is the graph d

Rotation about the origin is a transformation in which a point or object is rotated around the origin (0, 0) by a certain angle. The origin is the fixed point of the rotation, and all other points move in a circular path around the origin.

To perform a rotation about the origin, you need to know the angle of rotation, the coordinates of the point or object being rotated, and the direction of rotation (clockwise or counterclockwise).

Using the above as a guide, we have the following:

The graph after a rotation about the origin is the graph (d)

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a.

i. 10% of $110,000 = $11,000 down payment

ii. Loan (mortgage) = $110,000 - $11,000 = $99,000

iii. Monthly payment = P * r * (1 + r)n / ((1 + r)n - 1), where P represents the principal amount, r represents the monthly interest rate, and n represents the number of monthly installments.

First, we must determine the quantity of monthly payments. Because it is a 30-year loan, the monthly installments are 30 * 12 = 360.

The monthly interest rate of 9% divided by 12 equals 0.0075.

When we plug in the values, we get:

$793.07 monthly payment

iv. Loan total interest paid = (monthly payment * number of instalments) - principal amount = ($793.07 * 360) - $99,000 = $184,465.20

b

i. Reduction in loan balance = $99,000 - $88,536 = $10,464

ii. To date, the total amount paid to the loan firm is (monthly payment * a number of payments) = ($793.07 * 120) = $95,168.40.

We multiplied by 120 (rather than 10*12) because we're computing total payments made so far, not the total payments made over the life of the loan.

iii. Total interest paid thus far = total money given to the loan business minus principal amount = $95,168.40 - $99,000 = -$3,831.60

The negative figure shows that the interest paid thus far has been less than the principal amount. This is because, in the early phases of the loan, the majority of the monthly payment goes towards interest, with only a little portion going toward principal reduction.

iv. Home equity  = value of the home - remaining debt

= $150,000 - $88,536

= $61,464

c.

i. New monthly payment = P * r * (1 + r)n / ((1 + r)n - 1), where P represents the remaining loan value, r represents the new monthly interest rate (6% / 12 = 0.005), and n represents the number of monthly payments remaining (360 - 120 = 240).

When we plug in the values, we get:

$63.63 is the new monthly payment.

Total interest paid on the new loan during the life of the loan = (new monthly payment * number of payments) - remaining loan balance = ($63.63 * 240) - $88,536 = $32,028.40

d.

Monthly savings = old monthly payment minus new monthly payment = $793.07 - $63.63= $729.44

Total interest paid on the new loan during the life of the loan = (new monthly payment * number of payments) - remaining loan balance = ($63.63 * 360) - $88,536 = $37,847.80

Because the new loan is being paid off over a longer period of time, the total interest paid during the life of the new loan is more than the remaining interest on the previous loan.

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Answer:

Step-by-step explanation:

To compute the break-even sales (in barrels) for the current year, we need to first determine the contribution margin per barrel, which is the amount left over from the selling price of each barrel of beer after variable costs are subtracted.

Variable costs per barrel can be calculated as 75% of the cost of goods sold per barrel, which is:

Variable cost per barrel = (75% x Cost of goods sold) / Barrels sold

Variable cost per barrel = (0.75 x $1,628 million) / 37 million barrels

Variable cost per barrel = $33.00

Similarly, the variable marketing, general, and administration expenses per barrel can be calculated as:

Variable marketing, general, and administration expenses per barrel = (50% x Marketing, general, and administration expenses) / Barrels sold

Variable marketing, general, and administration expenses per barrel = (0.50 x $592 million) / 37 million barrels

Variable marketing, general, and administration expenses per barrel = $8.00

Therefore, the contribution margin per barrel is:

Contribution margin per barrel = Selling price per barrel - Variable costs per barrel

Contribution margin per barrel = $6,512 million / 37 million barrels - $33.00 - $8.00

Contribution margin per barrel = $98.00

To compute the break-even sales (in barrels) for the current year, we can use the following formula:

Break-even sales (in barrels) = Fixed costs / Contribution margin per barrel

Fixed costs can be calculated as:

Fixed costs = Income from operations + Variable marketing, general, and administration expenses x Barrels sold - Contribution margin per barrel x Barrels sold

Fixed costs = $4,292 million + $8.00 x 37 million barrels - $98.00 x 37 million barrels

Fixed costs = $1,108 million

Substituting this into the formula, we get:

Break-even sales (in barrels) = $1,108 million / $98.00 per barrel

Break-even sales (in barrels) = 11.29 million barrels

Rounding this to two decimal places and converting to millions, we get:

Break-even sales (in barrels) = 11.29 million barrels = 11.3 million barrels (rounded)

After multiplying (−3x+4) with (2x−1) we get a quadratic equation which is equal to −6x² + 11x − 4.

To multiply the expressions (−3x+4)(2x−1), we use the distributive property of multiplication:

(−3x+4)(2x−1) = −3x(2x) + 4(2x) − 3x(−1) + 4(−1)

Simplifying the above expression, we get:

= −6x² + 8x + 3x − 4

= −6x² + 11x − 4

Therefore, the product of (−3x+4)(2x−1) is −6x² + 11x − 4.

We can also use the FOIL method to multiply the two expressions:

(−3x+4)(2x−1) = −3x(2x) −3x(−1) + 4(2x) + 4(−1)

= −6x² + 3x + 8x − 4

= −6x² + 11x − 4

Either method can be used to get the same result.

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Answer:

Step-by-step explanation:

After 5 years at a simple interest rate of 10%, Patrick would have earned $500 in interest ($1000 x 10% x 5 years). So at the end of the 5 years, he would have $1500 in the account.

If this entire amount is deposited into a new account that earns 10% compounded quarterly, we need to determine the quarterly interest rate first.

The quarterly interest rate is (1 + 0.10/4)^4 - 1 = 0.025 (rounded to three decimal places).

After 10 years (or 40 quarters) at a quarterly interest rate of 0.025, the compounded amount is:

$1500 x (1 + 0.025)^40 = $4045.56

Therefore, Patrick would have $4045.56 in the account after 10 years when rounding to the nearest cent.

Hope that Helps :)