The Frequency table shows The time it look students in PE class to run in 1 mile

Answer:

The two numbers are 494 and 504

Step-by-step explanation:

Let x = one of the numbers

Let y = the other number

x + y = 998

x - y = 10   or x = y + 10

Substitute y + 10 for x in the first equation and solve for y

x + y = 998

y + 10 + y = 998  Subtract 10 from both sides

y + y = 988  Combine like terms

2y = 988  Divide both sides by 2

y = 494

One of the numbers is 494.

x = y + 10  Substitute 494 for y

x = 494 + 10

x = 504

The other number is 504.

Check:

x + y = 998

504 + 494 = 998

998 = 998 checks

x - y = 10

504 - 494 = 10

10 = 10 checks

Helping in the name of Jesus.

Answer:

Step-by-step explanation:

House

B) Down Payment: $151,800

C) $607,200

D) $819,720

E) $1,426,920

F) $47,564

Car:

B) $2,902.50

C) $16,447.50

D) $3,700.6875 = $3,700.69

E) $20,148.1875 = $20,148.19

F) $335.803125 = $335.80

DONE !!! :)

Answer:

-166/, -0.82,

Step-by-step explanation:

The above fraction, decimal are all evaluated answer for (11/16−(3/4)2)×1

Answer:

Four units left and one unit up

Step-by-step explanation:

Since we're subtracting from x, the figure is going to go toward the left side of the coordinate plane, and since we're adding to y, the figure is going to go up.

Let's start by setting up a proportion to represent the ratio of Illinois students to Michigan students:

Illinois students / Michigan students = 6/5

We can simplify this proportion by multiplying both sides by 5:

Illinois students = 6/5 * Michigan students

Next, we can use the information in the table to set up an equation that relates the number of Illinois students, Michigan students, and Indiana students:

Illinois students + Michigan students + Indiana students = 175

We can substitute the expression we obtained for the number of Illinois students into this equation:

6/5 * Michigan students + Michigan students + Indiana students = 175

Multiplying both sides by 5 to eliminate the fraction, we get:

6 * Michigan students + 5 * Michigan students + 5 * Indiana students = 875

Combining like terms, we get:

11 * Michigan students + 5 * Indiana students = 875

Now we can use the fact that the ratio of Illinois students to Michigan students is 6:5 to set up another equation:

Illinois students / Michigan students = 6/5

Substituting the values from the table, we get:

Illinois students / Michigan students = 24/20

Cross-multiplying, we get:

Illinois students * 20 = Michigan students * 24

Simplifying, we get:

Illinois students = 6/5 * Michigan students = 24/20 * Michigan students = 6/5 * 24 Michigan students = 28.8 Michigan students

Since the number of students must be a whole number, we can round 28.8 up to 29. This means that there were 29 Michigan students.

Substituting this into the equation we obtained earlier, we get:

11 * 29 + 5 * Indiana students = 875

Solving for Indiana students, we get:

5 * Indiana students = 875 - 11 * 29 = 546

Dividing both sides by 5, we get:

Indiana students = 546/5 = 109.2

Since the number of students must be a whole number, we can round 109.2 up to 110. This means that there were 110 Indiana students.

Therefore, the answer is 110 students from Indiana.

The coordinates of the midpoints of the given line segment is:

(3.5, 1.5)

The midpoint of a line segment is simply referred to as the center of that specific line segment.

Thus, the coordinates at that point will be referred to as the coordinates of the midpoint.

The coordinates of the endpoints of the line are:

(4,6) and (3,-3)

The formula to find the coordinates of the midpoint of the line is:

(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2

Thus, we have:

(x, y) = (4 + 3)/2, (6 - 3)/2

= (3.5, 1.5)

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The journal entry to record the transaction is given:

Account Debit Credit

Cash $464,000

Common Stock, $3 par value $87,000

Paid-in capital in excess of par  $377,000

A journal entry is used to record a business transaction in the accounting records of a business.

A journal entry is usually recorded in the general ledger. Alternatively, it may be recorded in a subsidiary ledger that is then summarized and rolled forward into the general ledger

Assuming the shares have a $3 par value and sell for $16 cash per share:

Cash reeived from issuance of 29,000 common shares = 29,000 x $16 = $464,000

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The contradicting statement is

B. I and III

The contradictory statement is that of I and III since the sum of angles in a triangle is always 180 degrees.

Given that

I. triangle ABC is a right triangle. say angle C = 90 degrees and

angle B = 103 degrees,

So the sum of the angles in the triangle would be:

= angle B + m angle C

= 103 + 91

= 194

This is against the law of angles of a triangle

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T(-1, 7)

→

T′(-1, -7)

U(-1, 8)

→

U′(-1, -8)

V(9, 6)

→

V′(9, -6)

We can see from the calculation that the angle of elevation of the building is 22.6 degrees.

The angle of elevation is the angle between the horizontal plane and the line of sight from an observer to an object that is above the observer's level. It is the upward angle from the observer's eye to the object being observed.

We have that;

Tan θ = 500/1200

θ = tan-1 (500/1200)

θ = 22.6 degrees

Thus the angle of elevation is obtained as 22.6 degrees as we can see here.

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An equation that can be used to determine the angle measure, in degrees, of angle DBC is 67 + n = 90.

The measure of n is equal to 23 degrees.

In Mathematics and Geometry, a complementary angle refers to two (2) angles or arc whose sum is equal to 90 degrees (90°).

By substituting the given parameters into the complementary angle formula, the sum of the angles is given by the following mathematical equation;

∠ABD + ∠DBC = 90

∠ABD + n = 90

67 + n = 90.

n = 90 - 67

n = 23°

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

A linear function would be the best fit for the given data because as x increase the y-values change linearly.

Rounded to the .5 the slope of the function is approximately 32.5

A linear relation means that any increase of 1 unit in the independent variable (x) has always the same impact in the other variable (y).

In this particular case, the increases in the y-value are:

56 - 24 = 32

88 - 56 = 32

122 - 88 = 34

The mean of that, rounded to .5, is (32 + 32 + 34)/3 = 32.5

So the change is almost the same one, then this seems to be a linear relation.

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The volume of a cylinder whose diameter measures 32 feet and has a height of 10 feet is equal to: C. 8,038.4 ft³.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

Note: Radius = diameter/2 = 32/2 = 16 ft.

By substituting the parameters, we have:

Volume of cylinder, V = 3.14 × 16² × 10

Volume of cylinder, V = 8,038.4 cubic feet.

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Answer:

70.7°

350 feet

Im not too sure about the last one

The values of m and b after evaluation is -2 and 23 under the condition that If x=3t+t² and y=7−2t, and  tangent to the curve at t=2.

In orde to evaluate the equation of the tangent to the curve at t=2, we have to calculate the slope of the curve at t=2.
The slope of the curve at t=2 is presented by the derivative of y with respect to x at t=2.
y = 7 - 2t
x = 3t + t²
dy/dx = -2
Then, the slope of the tangent to the curve at t=2 is -2.
Now we have to evaluate the point on the curve at t=2.
x = 3(2) + (2)² = 10
y = 7 - 2(2) = 3
So, the point on the curve at t=2 is (10,3).
Applying  point-slope form of equation of line:
y - y₁ = m(x -x₁)
Here,
m = slope and (x₁,y1) is a point on the line.
Staging m=-2 and (x₁,y₁)=(10,3),
y - 3 = -2(x - 10)
Applying simplification
y = -2x + 23
Then, the equation of the tangent to the curve at t=2 is y=-2x+23.
So, m=-2 and b=23.
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Based on the image, we can infer that the router cannot cover the kitchen area.

To calculate if the router covers the living room and kitchen area, we must identify the area that the router can cover. In this case, the router covers an area of 850 square feet. However, we must take into account that this area is counted around the router.

From the above, we can infer that the router has signal coverage of 14 meters around it, so it would only cover the living room area.

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Answer:

Step-by-step explanation:  find the circumference and then consider the shape (circle) after that get rid of options that don't make sense like 7.3 and 7.1, 8 for the radius might be too big leaving you with    7     (use a calculator if needed)

The dimensions of each rectangle are x by (x- y) and y by (x - y); option A and D

The area of each rectangle is x² - 2xy + y²  and x² - xy

The total area of the remaining figure is 2x² - 4xy + 2y²

This figure represents the difference of two squares in that x² - y² = (x + y)(x -y)

The area of each rectangle is:

x * (x- y) =  x² -xy

and

y * (x - y) = xy - y²

The total area of the remaining figure is:

x² -xy + xy - y² = x² - y²

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The probability of Casey selecting a tie that goes well with the sport coat is 0.517.

The probability of Casey selecting a tie that does not go well with the sport coat is 0.483

The probability of Casey selecting a tie that goes well with the sport coat is:

P(goes well) = 15/29

P(goes well) ≈ 0.517

The probability of Casey selecting a tie that does not go well with the sport coat is:

P(does not go well) = 1 - P(goes well)

P(does not go well) = 1 - 15/29 = 14/29

P(does not go well) ≈ 0.483

The odds in favor of the tie going well with the sport coat are:

P(goes well) : P(does not go well) = 15/29 : 14/29

P(goes well) : P(does not go well) = 15:14

The odds against the tie going well with the sport coat are:

P(does not go well) : P(goes well) = 14/29 : 15/29

P(does not go well) : P(goes well) = 14:15

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The airplane weigh if it is carrying 52 gallons of fuel will be, 2338 pounds

Let,

Weight of airplane = y

Amount of fuel = x

The general linear equation can be written as, y=mx + c, where, (m) is slope, and (c) is a constant.

It is given,

2091 = 14m + c ..... (1)

2312 = 48m + c ..... (2)

On subtracting, (1) with (2), we get

221 = 34m

m= (221/34)= 6.5

Now, on putting the value of (m) in (1), we get,

2091 = 14(6.5) + c

So,

c = 2000

Therefore, the linear equation can be written as,

y = (6.5)mx + 2000

Now to find the airplane weight at 52 gallons of fuel, we put x = 52, to find y.

That is,

y = (6.5)(52) + 2000

y = 2338

So, the airplane weigh if it is carrying 52 gallons of fuel will be, 2338 pounds.

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The solution is: x ≥ 6.

What is linear inequalities?

Linear inequality is an equation or expression that do not have a definite solution. Thus it consist of either of greater than, less than, greater than or equal to, less than or equal to etc.

In the given inequality question, we have;

8 is less than or equal to -3x +26

This can be expressed as;

8 ≤ -3x +26

so that collecting like terms,

8 - 26 ≤ -3x

-18 ≤ -3x

-18/ -3 ≤ x

6 ≤ x

Therefore, x ≥ 6.

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The length of the square with a diagonal of 32 cm is 22.6 cm.

A square is a plane shape with all sides and angles equal.

To calculate the length of the square from its diagonal, we use Pythagoras formula

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for l

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Answer: 134.

Step-by-step explanation:

First revert 67% into it's decimal form. You get 0.67. Then, multiply 0.67 by 200 because there were 200 problems.

0.67 x 200

67 x 2

134

So, christian got 134 out of 200 problems correct.

The value of the "trigonometric-expressions' are :

(a) tan(5π/2) is undefined,

(b) sec(315°) is √2.

Part(a) : The expression "tan(5π/2)" is undefined because the tangent function is undefined at odd multiples of π/2, which includes 5π/2.

Part(b) : To find the value of sec(315°), we use the identity: sec(θ) = 1/cos(θ),

First, we convert 315° to radians:

Which is : 315° = (7π/4) radians;

Next, we find the value of cos(7π/4):

⇒ cos(7π/4) = cos(π/4) = (√2)/2;

Finally, we substitute in the identity for sec(θ);

So, Sec(7π/4) = 1/cos(7π/4) = 1/[(√2)/2] = √2.

Therefore, value of sec(315°) is √2.

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The given question is incomplete, the complete question is

Find the value of the trigonometric expressions :

(a) tan(5π/2)

(b) sec(315°)

The age of the radioactive element of half-life 5750 years is 11047.8  years.

Radioactive elements are atoms that are unstable in normal conditions and are converted in another different atoms.

To calculate how old is the bone at the time it was discovered, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for t

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The amount of medication should they receive per dose is,

⇒ 363.6 mg

Given that;

A patient weighs 160 pounds and needs medication with dosage instructions of 15 mg/kg/day.

And, It is to be given in 3 doses each day.

Hence, We get;

1 pounds = 1/2.2 kg

160 pounds = 160 x 1/2.2 kg

                  = 72.72 kg

Since, It is to be given in 3 doses each day.

Hence, The amount of medication should they receive per dose is,

⇒ 72.72 x 15 / 3

⇒ 363.6 mg

Thus, The amount of medication should they receive per dose is,

⇒ 363.6 mg

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