Sarah ran 3,682 m yesterday on the track at her school. One time around the track is 263 m. Sarah wants to run 4,222 m today. Which number sentence can be used to calculate how many laps around the track Sarah should run today?

Answer:

14.3 sq units

Step-by-step explanation:

this shape is a trapezoid so we need to find height and each parallel base

to find height we can take the midpoint of RS and the midpoint of QP and then find the distance between each midpoint

midpoint of RS = (-3/2,2)

midpoint of QP = (2,-5/2)

distance between the two is 16/2 or 8

d(RS) = √2²+3² = [tex]\sqrt{13}[/tex]

d(QP) = √3²+6² = √45 = [tex]\sqrt{9}[/tex][tex]\sqrt{5}[/tex] or 3[tex]\sqrt{5}[/tex]

put values into the formula for area:

A = 1/2(8) + ([tex]\sqrt{13}[/tex] + 3[tex]\sqrt{5}[/tex])

A = 4 + ([tex]\sqrt{13}[/tex] + 3[tex]\sqrt{5}[/tex])

A ≈ 14.3

Answer:

the answer is C I hope you got this answer

Answer:

B 36

Step-by-step explanation:

DC^2=6^2+8^2. AD=9cm DB=6cm

DC^2=36+64

DC^2=100

DC=√100

DC=10cm

AC^2=15^2+8^2

AC^2=225+64

AC^2=289

AC=√289

AC=17

P OF TRIANGLE ADC=10+9+17

=36cm

The variable in 2x + 3 = 7 is x because rest 2, 3 and 7 are constant terms only x is the variable.

The meaning of such an equations in algebra is just a mathematical expression stating the equality between two mathematical terms. For instance, 6x + 5 = 11 is an equation where 6x + 5 and 11 are two expressions separated by the 'equal' sign.

Identity equations and conditional equations are the two types of equations. For just any value of both the variables, an equality remains true. Only such variables have values that make a condition expression true. Two expressions joined by an equals sign ("=") form an equation.

The variable in 2x + 3 = 7 is x because rest 2, 3 and 7 are constant terms.

if we solve the above equation, we get

2x + 3 = 7

or, 2x = 7 - 3

or, 2x = 4

or, x = 2

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Answer:

51.5g or A

I took a test with this question and got it right

Using the normal distribution, it is found that approximately 80% of the eggs on the farm have a mass greater than 51.5 g.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

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

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 55, \sigma = 4.2[/tex].

Approximately 80% of the eggs on the farm have a mass greater than the 20th percentile, which is X when Z = -0.84, hence:

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

[tex]-0.84 = \frac{X - 55}{4.2}[/tex]

X - 55 = -0.84 x 4.2

X = 51.5 g.

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====================================================

Explanation:

We set up a cosine ratio, since we want to connect the adjacent and hypotenuse. Then we'll use the inverse cosine, which is also known as arccosine, to isolate the angle value.

This is what your steps could look like:

cos(angle) = adjacent/hypotenuse

cos(L) = LM/LN

cos(L) = 18/60

cos(L) = 0.3

L = arccos(0.3)

L = 72.542396876278 which is approximate

L = 72.54 degrees approximately

Make sure your calculator is in degree mode.

Answer:

False

Step-by-step explanation:

Since it is a "one for one" deal, it would be direct variation as one varible is directly effecting another.

9514 1404 393

Answer:

  397.76 cm^2

Step-by-step explanation:

The area of the shaded region is the rectangle area less the area of the circle with diameter 8 cm. The area of the rectangle is

  A = LW . . . . for length L and width W

The area of the circle is ...

  A = π/4d^2 . . . . . for diameter d

Then the shaded area is ...

  A = (28 cm)(16 cm) - (π/4)(8 cm)^2 = 448 cm^2 -50.24 cm^2

  A = 397.76 cm^2

Answer:

136

Step-by-step explanation:

First you need to know that there are 2 triangles in the image.

One triangle (the smaller one) has sides that measure 119 (the side) and 56 (the bottom).

The other triangle (the bigger one) has sides that measure 119 + ? (the side) and 120 (the bottom).

Let's replace the 119 + ? with an x so that the entire side length of the big triangle measures x.

1. Make a proportion using ratios. For the ratios of each triangle, we can do side over bottom lengths and then set them equal to each other.

119  =    x              sides

56        120            bottoms

2. You can cross multiply, or just solve for x.

119*120= 14280

14280/56= 255

3. Then subtract the total length minus 119 to find the question mark

255 - 119 = 136

The ratios on the double line are 3:7, 6:14, 12:28 and 15:35.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given that, Lin makes her favorite juice blend by mixing cranberry juice with apple juice in the ratio shown on the double number line.

From the given double line, the ratio is 9:21.

Completed double line has the following ratios

3:7, 6:14, 12:28, 15:35

Therefore, the ratios on the double line are 3:7, 6:14, 12:28 and 15:35.

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Answer:

11. ∠5 and ∠7 are corresponding angles

12. ∠1 and ∠8 are alternate exterior angles

13. ∠3 and ∠6 are alternate interior angles

14. ∠6 and ∠7 are consecutive interior angles.

15. ∠1 = 58

    ∠2 = 122

    ∠3 = 58

    ∠5 = 122

    ∠6 = 58

    ∠7 = 122

    ∠8 = 58

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The area of the shaded regions is 4π + 4, which can be obtained by subtracting 2π - 4 from 3π. This is an exact value, with no further simplification required.

Step 1: Calculate the area of the entire circle.

A = πr^2

A = π(5)^2

A = 25π

Step 2: Calculate the area of the unshaded region.

A = πr^2

A = π(2)^2

A = 4π

Step 3: Subtract the area of the unshaded region from the area of the entire circle.

A = 25π - 4π

A = 21π

Step 4: Calculate the area of the shaded region.

A = 21π - (2π - 4)

A = 21π - 2π + 4

A = 19π + 4

A = 4π + 4

The area of the shaded regions can be found by subtracting the area of the unshaded region from the area of the entire circle. To find the area of the entire circle, we use the formula A = πr^2, where r is the radius of the circle. Plugging in r = 5, we get A = 25π. To find the area of the unshaded region, we use the same formula, but now with r = 2. This gives us A = 4π. Subtracting the area of the unshaded region from the area of the entire circle gives us A = 21π. We then subtract 2π - 4 from 21π to get the area of the shaded region, which is 4π + 4. This is an exact value, with no further simplification required.

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Answer: x4 2x 3 is 126x power of 3 + 5

Answer:

16 lawns

Step-by-step explanation:

set up a proportion:

(4/5 ÷ 1) = (x÷20)

cross-multiply:

5x = 80

x = 16

Kate can mow lawns at a constant rate of 16 lawns in 20 hour.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Kate can mow lawns at a constant rate of 4/5 lawns per hour.

Now,

Since, Kate can mow lawns at a constant rate of 4/5 lawns per hour.

Hence, In 20 hours;

Kate can mow lawns = 20 × 4/5

                                 = 16 lawns

Thus, Kate can mow lawns at a constant rate of 16 lawns in 20 hour.

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The y intercept of the graph of the function f(d) indicates f(d) = 11 and the average rate of change of the function f(d) from d = 2 to d = 7 is 0.114, making 6.97 a reasonable domain to depict the growth function.

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.

An equation is a mathematical expression with two equal sides and an equal sign in between. An equation is a mathematical statement proving the equality of two numbers or values.

Equations can be categorized as either identities or conditional equations. For each value of the variables, an identity holds true. Only specific values of the variables make a conditional equation true. An equals symbol ("="), separating two expressions, is used to represent an equation.

Part A:

11.79 = 11(1.01[tex])^d[/tex]

substitute the values in the above equation, we get

[tex]$$& (1.01)^d[/tex] = 11.79 / 11

simplifying the equation, we get

[tex]$$& (1.01)^d[/tex] = 1.071818

d = log 1.071818 / log 1.01

The value of d = 6.97

Part B:

y-intercept is obtained when domain = 0

[tex]$& d=0 \Rightarrow f(0)=11(1.01)^0=11 \times 1=11 \\[/tex]

f(d) = 11

Part C:

Average rate of change,

[tex]$\Delta \mathrm{f} / \Delta \mathrm{d} & =(\mathrm{f}(7)-\mathrm{f}(2)) /(7-2) \\[/tex]

[tex]$& =\left(11(1.01)^7-11(1.01)^2\right) / 5 \\[/tex]

= 0.57 / 5 = 0.114

The y intercept of the graph of the function f(d) indicates f(d)=11 and the average rate of change of the function f(d) from d=2 to d=7 is 0.114, making 6.97 a reasonable domain to depict the growth function.

The complete question is:

A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:

f(d) = 11(1.01)d

Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm. What is a reasonable domain to plot the growth function? (4 points)

Part B: What does the y-intercept of the graph of the function f(d) represent? (2 points)

Part C: What is the average rate of change of the function f(d) from d = 2 to d = 7, and what does it represent?

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6.97 is an appropriate domain in which to represent the growth function because the y intercept of the graph of the function f(d) suggests that f(d) = 11 and the average rate of change of the function f(d) from d = 2 to d = 7 is 0.114 as studied by biologist.

A mathematical statement that establishes the equality of two mathematical expressions is the definition of an equation in algebra.

A mathematical expression with two equal sides and an equal sign in the middle is called an equation. A mathematical statement establishing the equality of two numbers or values is called an equation.

Either identities or conditional equations are categories for equations. Each value of the variables corresponds to a specific identity. A conditional equation can only be true for a certain range of variable values. An equation is represented by two expressions being separated by the equals sign ("=").

Part A:

11.79 = 11(1.01

substitute the values in the above equation, we get

[tex](1.01)^{d}[/tex] = 11.79 / 11

simplifying the equation, we get

  (1.01)^{0} = 1.071818

d = log 1.071818 / log 1.01

The value of d = 6.97

Part B:

y-intercept is obtained when domain = 0

d = 0

f(0) = 11[tex](1.01^{0} )[/tex] = 11 * 1 = 11

f(d) = 11

Part C:

Average rate of change,

Δf / Δd  = (f(7) - f(2)) / 7-2

= 0.57 / 5 = 0.114

The y intercept of the graph of the function f(d) indicates f(d)=11 and the average rate of change of the function f(d) from d=2 to d=7 is 0.114, making 6.97 a reasonable domain to depict the growth function.

The complete question is:

A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:

f(d) = 11(1.01)d

Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm. What is a reasonable domain to plot the growth function? (4 points)

Part B: What does the y-intercept of the graph of the function f(d) represent? (2 points)

Part C: What is the average rate of change of the function f(d) from d = 2 to d = 7, and what does it represent?

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Parallelogram M'N'P'Q' is larger than parallelogram MNPQ because MN and M'N' have lengths of 2 and 5 respectively, and parallelogram MNPQ is dilated by a factor of 5/2 to give parallelogram M'N'P'Q'.

A parallelogram is a straightforward quadrilateral in Euclidean geometry that has two sets of parallel sides. In a particular kind of quadrilateral known as a parallelogram, both sets of opposite sides are parallel and equal. There are four different kinds of parallelograms, including three unique kinds. Parallelograms, squares, rectangles, and rhombuses are the four different shapes. Having two sets of parallel sides makes a quadrilateral a parallelogram. In a parallelogram, the opposing sides and angles are both the same length. On the same side of the horizontal line, the interior angles are additional angles as well. 360 degrees is the total number of interior angles.

To make parallelogram M'N'P'Q, parallelogram MNPQ was enlarged.

Points include M(2, 2), N(4, 2), P(3, 3), and Q. (1,-3)

M'(5, 5), N'(10, 5), P'(8, 7), and Q' (3,-7)

A) First, determine Minnesota's length:

|MN| = 2

|M'N'| = 4

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7th interval is not perfect

7th interval is not perfect

A (real) interval in mathematics is a collection of real numbers that includes all real numbers that fall within any two of the collection's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 ≤ x ≤1. The group of numbers such that 0 < x< 1 and the group of all real numbers are other examples of intervals.

the empty set, any singleton, the set of positive real numbers, the set of nonnegative real numbers, and (set of one element).

Real intervals are the simplest sets whose "length" (or "measure" or "size") is straightforward to define, making them significant in the theory of integration. The Borel measure and ultimately the Lebesgue measure can subsequently be produced by applying the concept of measure to more intricate sets of real numbers.

Interval arithmetic is a broad numerical computing method that automatically generates assured enclosures for all formulas, even in the presence of errors, approximations in mathematics, and arithmetic roundoff.

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The equation that represents the relationship of x number of badges to y dollars is y = 9x.

What is an equation?

A mathematical statement called an equation displays the equality of two mathematical expressions. Variables, coefficients, exponents, arithmetic operators, equal signs, and constants are some of the components that make up an equation.

 An equation is said to be linear if the maximum power of the variable is consistently 1.

Let the number of badges be x and the cost of x number of badges be y.

From the question, we know that for 48 badges, the cost is $432.

So the cost of one badge = 432/48 = $9

Now the cost of x number of badges = $(9x)

We mentioned in the beginning that the cost of x number of badges is y

Therefore the equation that represent the relationship of x badge to y dollars is,

        y = 9x

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Answer:

25.5

Step-by-step explanation:

Each year the tree grows by 6 inches.

Answer:

26

Step-by-step explanation:

The increase per year is 6.5 which can be derived by subtracting the first year from the second year:

13-6.5=6.5

then subtracting the second year from the third to confirm

19.5-13=6.5

So now we know the increase all we do is add:

19.5+6.5=23

Method 2: A slightly more complicated method of solving is via a linear equation which in this scenario is Hⁿ=6.5N (the n means the nth term) and then we plug 4 into it to get Hⁿ=26

Answer:

Pitcher 2

Step-by-step explanation:

Pitcher 1  = 4 x 1.25 = 5ml concentration

Pitcher 2 = 5 x 2 = 10ml concentration

therefore, pitcher 2 has more concentration :)

hope this helped

Answer:

So I would say when the number of classes is lower fishing is less expensive and when the number of canoeing classes is lower it's less expensive

Step-by-step explanation:

You have to make sure to pay attention to the label and the points in the graph and the table

Answer:

47.8 MB

Step-by-step explanation:

17.5% = 0.175

273 * 0.175 = 47.775

Rounded

47.8 MB

Answer:

x = 15

y = 7.5

Step-by-step explanation:

✔️Diagonals of a parallelogram bisect each other at 90°.

Therefore,

2x° + 60° + 90° = 180° (sum of triangle)

Solve for x

2x + 150 = 180

2x = 180 - 150

2x = 30

2x/2 = 30/2

x = 15

✔️2x = 4y (alternate angles/corresponding angles)

Plug in the value of x

2(15) = 4y

30 = 4y

30/4 = y

7.5 = y

y = 7.5

Answer:  There are 108 hammers, and there are 36 screwdrivers. 36×3=108·

Step-by-step explanation: We know that there are more hammers than screwdrivers, so there are 36 screwdrivers but there are 3 times as many hammers so we multiply 36 by 3 to get 108.

Answer:

Step-by-step explanation:

you will take the number from one dice and the number from the other dice and simply add them together. so if one dice equals 4 and the other is 1 you would lay it out as 4+1=5 hope this helps

Answer:

i. 2000 ii. 3500

Step-by-step explanation:

Since the absolute value of a number x, |x| = x if x > 0 and |x| = -x if x < 0,

i. Absolute value of Mountain Summit

Since the Mountain Summit elevation, x = 2000 - 0 = 2000, its absolute value = |2000| = 2000

ii. Absolute value of Mountain Overlook

Since the Mountain Summit elevation, x = -3500 - 0 = -3500, its absolute value = |-3500| = -(-3500) = 3500

Answer:

Step-by-step explanation:

[tex]\sqrt{61}[/tex]

To solve 3 composite functions, you would need to break each function down into its individual components. Then, you would need to combine each component one at a time, starting with the outermost function and working your way inwards.

1. Break each function down into its individual components. This may involve splitting them into simpler functions such as polynomials, exponentials, trigonometric functions, and so on.

2. Start with the outermost function and combine each component one at a time. Make sure to apply the order of operations to each step in order to get the correct result.

3. Evaluate the combined function. This means solving for the output of the function, which may involve plugging in values for certain variables.

4. Repeat the same process for the other two functions.

5. When you have evaluated all three functions, you can combine the results of each to get the answer to the composite functions.

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Answer:

22°

Step-by-step explanation:

a right angle have 90°

So

x+68°=90°

=>x=90-68

=22°