Let f(x) = 5x - x+1 and g(x) = -3x. Evaluate the composition (f • g)(1).

Answer:

8000 litres

Step-by-step explanation:

⅓ (4 × 2.5 × 2.4)

= 8 m³

1 m² = 1000 litres

8 m³ = 8000 litres

The volume of water in the tank in litres can be found by calculating one third of the capacity of the tank in cubic metres and then multiplying that by 1000. We represent this as 1000X/3 litres, where X is the total capacity of the tank in cubic metres.

To solve this problem, we firstly need to know the total capacity of the tank in cubic metres. Since we don't have this specific information in the question, let's call this capacity as 'X' cubic metres.

One third of the tank is filled with water, so the volume of water in the tank is one third of X, which is (1/3) * X cubic metres. We know that 1 cubic metre is equivalent to 1000 litres, therefore, the volume of the water in the tank in litres is (1/3) * X * 1000, which simplifies to 1000X/3 litres.

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Answer:

"Integrated science is defined as a cumulative approach of scientific study that synthesizes the per- spectives of the individual disciplines, and integrates them during all phases of the approach to a question or problem, with the results having an influence on policy and management decision".

Step-by-step explanation:

*Hope this helps*

Science is a systematic study of the natural world that relies on evidence and logical testing of ideas, including various disciplines such as physics, chemistry, and biology.

Science is a systematic examination of the natural world's structure and functioning, including its physical and biological attributes. It is a process of gaining knowledge based on evidence and logical testing of ideas. Natural sciences encompass physics, chemistry, biology, geology, and astronomy and use mathematics and logic as part of their methodologies.

Given Evelyn's hourly rates for both of her jobs and the total number of working hours she has, Evelyn can work a maximum of 7 hours tutoring if she has already spent 8 hours lifeguarding.

To solve this problem, we first calculate the total earning from lifeguarding by multiplying the hourly rate by the number of hours she worked, which results in $18 * 8 = $144. The minimum total earning she must make is $200, so she still needs to earn $200 - $144 = $56. Since she is making $11 per tutoring hour, she will need to work a minimum of $56 / 11 which is approximately 5 hours. However, these are still part of the total of 15 hours maximum she can work, and she has already worked 8 hours lifeguarding, meaning she can work at most 15 - 8 = 7 hours tutoring in the remaining time.

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The maximum number of whole hours tutoring that Evelyn can work while still meeting her requirements is 5 hours.

To solve this problem, we can use a combination of inequalities to represent the given constraints.

We need to solve these inequalities simultaneously to find the maximum number of whole hours Evelyn can work as a tutor.

1. The first inequality:

[tex]\[ x + 8 \leq 15 \][/tex]

[tex]\[ x \leq 15 - 8 \][/tex]

[tex]\[ x \leq 7 \][/tex]

2. The second inequality:

[tex]\[ 18(8) + 11x \geq 200 \][/tex]

[tex]\[ x \geq \frac{56}{11} \][/tex]

[tex]\[ x \geq 5.09 \][/tex]

Since the number of tutoring hours must be a whole number, Evelyn can work a maximum of 5 whole hours tutoring and still meet her requirements.

Therefore, the maximum number of whole hours tutoring that Evelyn can work while still meeting her requirements is 5 hours.

Answer:

It would be a point which is at (-4,-7).

The image of the point (4,-7) after a reflection over the y-axis is (-4,-7). This happens because the y-axis is the axis of symmetry during a reflection over this axis, changing the x-coordinate's sign while keeping the y-coordinate constant.

The image of a point after a reflection over the y-axis results in the x-coordinate of the point changing its sign. Therefore, the image of the point (4,-7) after a reflection in the y-axis would be (-4,-7). In other words, you move the point 4 units to the left across the y-axis while the y-coordinate remains unchanged.

This process is derived from the concept that the y-axis is the axis of symmetry in a reflection over the y-axis. As such, points on one side of the axis are mirrored on the other side, changing only the sign of the x-coordinate and keeping the y-coordinate constant.

A helpful way to visualize this is by drawing a coordinate grid and plotting the point (4,-7). By reflecting this point over the y-axis, you will see it lands at the point (-4,-7).

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Answer:

2600 were tested

99.6% of 2590 = - 10 + 10  = 2600 people.

99.6% of 2600 = 2589.6

Step-by-step explanation:

10 = positive = inverse of 99.6 = 0.4

0.4 x 1000 = 400

So we need an odd number ie) 3,000 minus 400 to make 10 extra when inverse is missing. = 3000 - 400 = 2600

99.6% of 2600 = 2589.6

Is the lowest number.

The measure of ∠B is 119°.

An exterior angle is a measure of rotation between one extended side(we extend it virtually) of the polygon with its adjacent side which is not extended.

All the exterior angles are of the same measure, and therefore, their measure is (360/n)°.

The angle adjacent to 112° will form a straight angle along with 112° adding to 180° which makes ∠C=68°

Then;

a+c+51°= 180°

a+68°+51° = 180°

a+119° = 180°

a = 180° - 119°

a = 61°

Now,

a+b = 180°

61+b = 180

b = 180-61

b = 119°

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Answer:

119

Step-by-step explanation:

100 on edge

Answer:707.63

Step-by-step explanation:

Answer:798.94

Step-by-step explanation:

Let's try a line

y = mx + b

From (0,4):

4 = 0x + b

b = 4

So far we have

y = mx + 4

From (1,1)

1 = m(1) + 4

-3 = m

Our rule is y = -3 x + 4

Let's check the other points:

-3(-4)+4 = 12+4 = 16 good

-3(4)+4 = -12+4 = -8 good

-3(9) + 4 = -23  good

Answer: y = -3 x + 4

The rule matching a function as shown by a table can be determined by analyzing the difference and relationship between x-values and y-values. This might represent a linear, exponential, or quadratic relationship, which can be described by a range of mathematical equations.

Unfortunately, without having the actual table and data, it is hard to give an accurate rule for the function. However, generally, in order to define a rule that matches a function represented by a table, you would need to discern a pattern between the inputs (often represented by the x-values) and the outputs (represented by the y-values).

In some cases, this might be a simple linear rule where each step in the x-values increases or decreases the y-values by a consistent rate; this would represent a formula of the format y = mx + b, where m is the change in y over the change in x, and b is the y-value when x = 0. Alternately, more complex relationships (such as exponential or quadratic rules) might be represented and would need different formulas to be described properly.

Determining the rule can often involve finding the rate of change between pairs of data points and discerning what kind of relationship this reveals. The explanation and answer would then match this established pattern.

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Answer:12.5h

Step-by-step explanation:

First, you would add 5+3+4.5. This equals 12.5. H represents her hourly pay rate. In order to find how much she earned, you would have to multiply 12.5(h).

Answer:12.5h

Step-by-step explanation:

Minimum price: Increases.

Maximum price: Remains the same.

Range: Increases.

Mean (Average) price: Cannot be determined.

When the kid's meal is added to the menu, the effect on the statistics of the meal prices can be determined as follows:

Minimum Price: Increases

Adding the kid's meal, which costs $2.35, to the menu will increase the minimum price.

Therefore, the value of the minimum price statistic will increase.

Maximum Price: Increases

Since the maximum price of the kid's meal ($2.35) is lower than the previous maximum price of $12.10, adding the kid's meal to the menu will not change the maximum price.

Therefore, the value of the maximum price statistic remains the same.

Range: Increases

The range is calculated as the difference between the maximum and minimum prices.

As the minimum price increases while the maximum price remains the same, the difference between them (the range) will increase.

Therefore, the value of the range statistic will increase.

Mean (Average) Price: Cannot be determined

To determine the effect on the mean price, we would need information about the number of meal options available and their individual prices. Without this information, we cannot determine whether the mean price will increase, decrease, or remain the same.

Therefore, the value of the mean price statistic cannot be determined.

In summary:

Minimum price: Increases

Maximum price: Remains the same

Range: Increases

Mean (Average) price: Cannot be determined

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Given a volume of 4500π cubic feet, the radius is found to be approximately 15 feet after solving the equation.

To find the radius of a sphere given its volume, we use the formula for the volume of a sphere: V = (4/3)πr³. In this case, the given volume is 4500π cubic feet. To solve for the radius, we can set up the equation as follows:

V = (4/3)πr³

4500π = (4/3)πr³

To isolate r³, we divide both sides by π and then multiply by 3/4:

4500 = (4/3)r³

(3/4) * 4500 = r³

3375 = r³

Now, we take the cube root of both sides to find the radius:

r = ³√3375

r ≈ 15 feet

Therefore, the radius of the sphere is approximately 15 feet.

the radius of the sphere is 15 feet.

The formula for the volume [tex](\( V \))[/tex] of a sphere in terms of its radius [tex](\( r \))[/tex] is:

[tex]\[ V = \frac{4}{3}\pi r^3 \][/tex]

Given that the volume of the sphere is [tex]\( 4500\pi \)[/tex] cubic feet, we can set up the equation:

[tex]\[ 4500\pi = \frac{4}{3}\pi r^3 \][/tex]

To find the radius [tex]\( r \)[/tex], we need to isolate it in the equation. First, let's cancel out [tex]\( \pi \):[/tex]

[tex]\[ \frac{4500\pi}{\pi} = \frac{4}{3} r^3 \][/tex]

[tex]\[ 4500 = \frac{4}{3} r^3 \][/tex]

Now, to solve for [tex]\( r \)[/tex], we'll multiply both sides by [tex]\( \frac{3}{4} \)[/tex] to isolate [tex]\( r^3 \):[/tex]

[tex]\[ r^3 = \frac{4500 \times 3}{4} \][/tex]

[tex]\[ r^3 = \frac{13500}{4} \][/tex]

[tex]\[ r^3 = 3375 \][/tex]

Now, to find ( r ), we'll take the cube root of both sides:

[tex]\[ r = \sqrt[3]{3375} \][/tex]

[tex]\[ r = 15 \][/tex]

So, the radius of the sphere is 15 feet.

Given:

Original figure and enlarged figure

To find:

Which ratios can be used to find the scale factor.

Solution:

Scale factor is the ratio of comparing the corresponding sides of two figures.

Option A:

[tex]$ \text {Scale factor} =\frac{\text { Enlarged }}{\text { Original }}=\frac{6.5}{3.25}$[/tex]

Length of enlarged side = 6.5

Length of original side = 3.25

It is correct.

Option B:

[tex]$\text {Scale factor}= \frac{\text { Enlarged }}{\text { Original }}=\frac{3.25}{6.5}$[/tex]

3.25 is the length of original figure. But here it is mentioned in enlarged.

So, it is not correct.

Option C:

[tex]$\text {Scale factor }=\frac{\text { Enlarged }}{\text { Original }}=\frac{3}{1.5}$[/tex]

Width of enlarged side = 3

Width of original side = 1.5

It is correct.

Option D:

[tex]$\text{Scale factor} =\frac{\text { Enlarged }}{\text { Original }}=\frac{1.5}{3}$[/tex]

1.5 is the width of original figure. But here it is mentioned in enlarged.

So, it is not correct.

Option E:

[tex]$\text{Scale factor}= \frac{\text { Enlarged }}{\text { Original }}=\frac{1.5}{3.25}$[/tex]

1.5 is the width of original figure. But here it is mentioned in enlarged.

So, it is not correct.

Therefore the ratios can be used to find the scale factor are:

[tex]$ \text {Scale factor} =\frac{\text { Enlarged }}{\text { Original }}=\frac{6.5}{3.25}\ \text{and }\ \text {Scale factor }=\frac{\text { Enlarged }}{\text { Original }}=\frac{3}{1.5}$[/tex]

Answer:

A C

Step-by-step explanation:

Answer:

The answer is 1680m3

Step-by-step explanation:

h×b×1/2×w

Answer: The answer is 175

Step-by-step explanation:

Answer:

175

Step-by-step explanation:

Answer:

For the first part the intercept is -1 and the second part the anwser is -5

Step-by-step explanation:

This is becuase when dealing with slopes and the slope intercept form (y=mx+b) whatever is B in the said equation your are dealing with is the y intercept

Answer:

The answer is 67.5

Step-by-step explanation:

Answer: 135 miles

Step-by-step explanation: I am quick mafs

Answer:

154.29

Step-by-step explanation:

The area of rectangle is given by

Ar=lw

Area of semi circle is given by

[tex]A_c=0.5\pi r^{2}[/tex]

Since there are two semi-circles then the area will be

[tex]A_c=2*0.5\pi r^{2}=\pi r^{2}[/tex]

The diameter is given as 8 units hence the radius is half the diameter, 4 units

Length is given as 13 units and width is diameter which is equal to 8 units

Area of rectangle will be 13*8=104 square units

Area of the two semi-circles will be

[tex]A==\pi 4^{2}=50.285714285713[/tex]

Total area wi be 104+50.285714285713=154.285714285713 square units

Rounded off as 154.29 square units

Answer:

The answer is 154.3

Using the cosine ratio, side BC in the right-angled triangle is approximately 19.4 cm when rounded to three significant figures.

In the right-angled triangle ABC, where angle A is 90 degrees, side AB is the base, side AC is the perpendicular, and side BC is the hypotenuse, we can use trigonometry to find the length of BC.

The cosine ratio (cos) relates the adjacent side to the hypotenuse in a right-angled triangle. In this case, cos(B) = AB/BC. To find BC, rearrange the formula to BC = AB/cos(B).

Given AB = 6.3 cm and angle B = 71 degrees, substitute these values into the formula:

[tex]\[ BC = \frac{6.3 \, \text{cm}}{\cos(71^\circ)} \][/tex]

Using a calculator, find that cos(71 degrees) is approximately 0.325. Now, divide 6.3 cm by this value:

[tex]\[ BC \approx \frac{6.3 \, \text{cm}}{0.325} \approx 19.385 \, \text{cm} \][/tex]

Rounded to three significant figures, the length of side BC is approximately 19.4 cm.

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The simplified form of the expression √(-16) + √(-25) + 5 is 5 + 9i, where i represents the imaginary unit.

The student has asked to simplify the expression Sq -16+sq-25+5. This appears to be a typo, and I believe they are referring to square roots. The correct mathematical expression to simplify should be √(-16) + √(-25) + 5. The simplification of the square roots involving negative numbers results in imaginary numbers because the square root of a negative number is not defined in the set of real numbers but rather in complex numbers. For the given expression, complex numbers and imaginary units ('i', wherein i^2 = -1) will be introduced in simplification:

When we add these results with 5, we obtain 5 + 4i + 5i, which simplifies to 5 + 9i.

The number of apples Tyler purchased is the dependent variable.

The alphabetic character that expresses a numerical value or a number is known as a variable in mathematics.

A representation of an unknown numerical value in an equation or algebraic statement by a symbol, typically a letter. A variable can be defined as a quantity that is changeable and not fixed.

Given:

Tyler’s grocery receipt shows a charge of $0.25 for every apple he purchased.

'g' represent the amount on the grocery receipt.

'a' represent the number of apples purchased.

Therefore, 'a' is the variable here.

So, the amount of apple is independent variable but the purchased values if dependent variable.

Thus, the number of apple Tyler purchased is the dependent variable.

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Final answer:

The independent variable is the number of apples purchased, as it determines the dependent variable, which is the total amount spent on apples in the grocery bill.

Explanation:

The independent variable in this scenario is the number of apples purchased (represented by a). This is because the independent variable is the one that is changed or controlled in a scientific experiment to test the effects on the dependent variable. In this case, Tyler decides how many apples to buy, and that decision directly affects the total cost, which is the dependent variable (g). The price of an apple, the weight of the apples, and the amount on the grocery bill are all dependent on the number of apples Tyler chooses to purchase. To find the total amount spent on apples, one would multiply the number of apples purchased by the cost per apple.

Answer:

1

Step-by-step explanation:

Use PEMDAS

(Solve division first)

9 - 9 + 1 =

(Solve from left to right)

1

The slant height of the cone is 39.7 cm

Explanation:

Given:

Lateral surface area of a cone = 558π cm²

Radius, r = 31 cm

Slant height, l = ?

We know:

[tex]A = \pi r\sqrt{h^2+r^2}[/tex]

Where,

h is the height of the cone

r is the radius

Solving the equation further:

[tex]558\pi = \pi r\sqrt{h^2+r^2} \\\\558 = 31\sqrt{h^2+(31)^2} \\\\(18)^2 = h^2 + 961\\\\324 = h^2+ 961\\\\h = 25.23[/tex]

Lateral height, H = ?

Applying pythagoras theorm,

(H)² = (h)² + (r)²

(H)² = (25.23)² + (31)²

(H)² = 636.55 + 961

(H)² = 1597.55

H = 39.7 cm

Therefore, the slant height of the cone is 39.7 cm

Answer:

A

Step-by-step explanation:

Imagine folding the graph in half on the x-axis and tracing the shape on the other side.

Ps. x-axis is horizontal (left-right), y-axis is vertical (up-down)

The figure that represents the image of trapezoid LMNP after a reflection across the x-axis is the figure A

From the figure, we can see that the trapezoid LMNP is the second quadrant.

A reflection across the x-axis will place the trazpezoid in the third quadrant

The figure A is in the third quadrant

Hence, the figure that represents the image of trapezoid LMNP after a reflection across the x-axis is the figure A

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Answer:

t = -1

Step-by-step explanation:

-4 = 2t - 2

2t = -2

t = -1

Can I get brainliest

Answer:

t = -1

Step-by-step explanation:

-4 = 2t - 2

Add 2 on both sides.

-4 + 2 = 2t - 2 + 2

-2 = 2t

Divide both sides by 2.

-2/2 = (2t)/2

-1 = t

Answer:

13 and 8

Step-by-step explanation:

pls mark this brainliest im trying to lvl up

The two numbers that add up to 21 but subtract to 5 are 13 and 8.

The two numbers are 13 and 8.

To find the numbers, set up the system of equations:
x + y = 21 (Equation 1)
x - y = 5 (Equation 2)

Adding Equation 1 and Equation 2, you get 2x = 26, which means x = 13.

Substituting x back into Equation 1 gives y = 8.

Answer:

5:00

Step-by-step explanation:

1 hour 21 minutes = 1,35 hours

30 minutes = 0,5 hours

1,35-0,5=0,85 hours he needs to get to school

7-0,85=6,15

6,15 = 6 hours 9 minutes

In 6 hours 9 minutes he needs to leave the house

Answer:

70

Step-by-step explanation:

Dividing is multiplying by the reciprocal.

So 30 divided by 1/2

is like 30(2)=60

Then add 10 so 60+10=

70

The equivalent value of the expression "dividing 30 by half and adding ten"  is 70.

Given data:

Regarding step-by-step dissecting of "dividing 30 by half and adding ten"

Step 1 is to divide 30 in half.

A number is effectively divided by 1/2 when we divide it in half. A fraction's reciprocal is what you multiply by when you divide by it. 1/2 has a reciprocal of 2/1, or only 2.

As a result, multiplying 30 by 2 is equivalent to dividing it in half:

To make the equation simpler:

30 ÷ (1/2) = 30 × 2

= 60

Step 2: Ten-folding.

We obtain 60 by dividing 30 in half.

Now double the outcome by ten:

60 + 10 = 70

So, when you multiply 30 by half, add 10, and you get 70.

Hence, the equation is solved and the solution is 70.

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Answer:

I believe this is the answer your looking for? 22 + 2y

Step-by-step explanation:

Answer:

To use the distributive property, distribute multiplication by 2 to both terms inside the parentheses.

The products are 2(11) and 2(y).

The equivalent expression is 22 + 2y.

Step-by-step explanation:

hope this helps!