Last year, Rina's history and math classes had regular tests. Each history test had 14
questions and each math test had 11 questions. If Rina had to answer the same number of
history questions and math questions last year, what is the smallest number of each type of
question she must have answered?
​

Answer:

Radius  =  7 cm

Diameter  =  7 cm  ×  2  =  14 cm

Step-by-step explanation:

The radius of the circle is 7 cm, and the diameter is 14 cm.

Given that the radius (R) of a circle is 7 cm, we can determine both the radius and diameter of the circle.

Radius: The radius is the distance from the center of the circle to any point on its boundary. Thus, the radius provided is 7 cm.

Diameter: The diameter is twice the radius, as it stretches from one edge of the circle to the other, passing through the center. Therefore, the diameter is calculated as follows:

Diameter = 2 × Radius

Diameter = 2 × 7 cm

Diameter = 14 cm

So, the diameter of the circle is 14 cm.

To summarize, the radius is 7 cm and the diameter is 14 cm.

Answer: The height of the tree is 64.94ft

Step-by-step explanation:

Using the trigonometry of angles

Tan theta = opposite/adjacent

Tan 33° = height of the tree/100

Height of the tree= tan 33° * 100

= 0.6494*100

= 64.94ft

The height of the tree is 64.94ft

-1

Step-by-step explanation:

because 1 - 2 is -1

Answer: while earning interest at this rate, the total balance that will be found in the account will be $15,500

Step-by-step explanation:

Before calculating the amount that the sum will grow to after two years, we need to input the formula for calculating simple interest since what the pension fund agreed to pay is a simple if interest if 12%.

Simple interest (S.I) = [Principal(P) × Rate(R) × Time(T)]/100

In this case, the amount deposited initially us $12,500, this is therefore the principal (P). The pension fund agreed to pay a simple interest of 12%, this is then the rate(R). The investment is for a period of two years, this is the time, (t).

S.I = (12,500 × 12 × 2)/100

= $3,000

This is the total interest the deposit will yield. We then add this interest to the initial deposit of $12,500 to find the total amount that will now be in the account after the two years.

$12,500 + $3,000

= $15,500

The total balance in the account after the period of two years is $15,500

Final answer:

$15,500.

Explanation:

Danny is looking to calculate the final balance of his pension fund after two years of earning simple interest at a rate of 12% annually on a principal investment of $12,500. To determine the final balance, we need to use the formula for calculating simple interest:

Simple Interest = Principal × Interest Rate × Time

In this case, Principal is $12,500, the Interest Rate is 12% per year (or 0.12 when converted to a decimal), and Time is 2 years. So the calculation would be as follows:

$12,500 × 0.12 × 2 = $3,000

This means that the interest earned over two years is $3,000. To find the total balance after two years, this interest amount is added to the original deposit:

$12,500 + $3,000 = $15,500

Answer:

-4x+2

Step-by-step explanation:

rewright factor and reduce

Answer:

675 ft (3 s.f.)

Step-by-step explanation:

Please see attached picture for full solution.

m∠R = 110° and m∠S = 110°

Solution:

Given data:

RSWY is a parallelogram.

∠R = (5x – 90)° and ∠S = (2x + 30)°

In RSWY, ∠R and ∠S are opposite angles.

Opposite angles of a parallelogram are congruent.

m∠R = m∠S

(5x – 90°) = (2x + 30)°

5x° – 90° = 2x° + 30°

Add 90° on both sides of the equation, we get

5x° = 2x° + 120°

Subtract 2x° on both sides of the equation, we get

3x° = 120°

Divide by 3 on both sides of the equation.

x° = 40°

Substitute x = 40 in m∠R and m∠S.

m∠R = (5x – 90)°

         = 5(40°) – 90°

m∠R = 110°

m∠S = (2x + 30)°

         = 2(40°) + 30°

m∠S = 110°

Hence m∠R = 110° and m∠S = 110°.

Answer:

Step-by-step explanation:

a) no angles are described or shown

__

b) Opposite sides are the same length, so we have ...

  3x -21 = 34

  3x = 55 . . . . . . . add 21

  x = 55/3 = 18 1/3 . . . . . divide by 3

and

  4y +32 = 62

  4y = 30 . . . . . . . . subtract 32

  y = 15/2 = 7 1/2 . . . . divide by 4

__

c) The perimeter is the sum of the side lengths, so is ...

  P = 2(L+W) = 2(62 +34) = 192 . . . units

The area is the product of adjacent side lengths, so is ...

  A = LW = 62·34 = 2108 . . . square units

The value of x is approximately 5.4 when x^3 -10x = 100

The equation is given as:

x^3 -10x = 100

Using trial by error, we keep testing for the value of x that is true for x^3 -10x = 100

After several attempts, we have:

x = 5.4 (approximately)

Substitute 5.4 for x in x^3 -10x = 100

5.4^3 -10 * 5.4 = 100

Evaluate

103.5 = 100

Approximate

100 = 100

This means that x is approximately 5.4 when x^3 -10x = 100

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A solution to the equation x^3 −10x=100 using the trial and improvement method is approximately x=5.3 (rounded to 1 decimal place).

let's use the trial and improvement method to find a solution for the equation

x^3 −10x=100.

Start with a reasonable guess for x. In this case, it's often helpful to start with small integers.

Substitute the guess into the equation and see if it satisfies the equation.

Let's try

5^3 −10×5=125−50=75

The result is not equal to 100. Since the result is less than 100, we need to increase our guess.

Let's try

6^3 −10×6=216−60=156

The result is still not equal to 100. Since the result is now greater than 100, we need to decrease our guess.

Let's try

5.5^3 −10×5.5=166.375−55=111.375

This result is still greater than 100, so we need to try a smaller value.

5.2^3 −10×5.2=140.608−52=88.608

Now, this result is closer to 100. We can continue to refine our guess.

Let's try

5.3^3 −10×5.3=150.097−53=97.097

This result is getting closer to 100. We can keep refining our guess, but for the sake of brevity, let's stop here.

So, a solution to the equation x^3 −10x=100 using the trial and improvement method is approximately x=5.3 (rounded to 1 decimal place).

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Answer:

A. Strong negative

General Formulas and Concepts:

Statistics

Step-by-step explanation:

According to the graph and the data set, we can see that we do indeed have a negative correlation trend. Therefore, options B and D can be eliminated.

Looking at the graph, we can see that we can definitely tell that it is a negative slope and it would be pretty steep. Therefore, the best answer choice would be A. Strong negative.

Answer:

9802.9

Step-by-step explanation:

find 17.4% of 8350 and then add that to the original price

Answer:

$3150

Step-by-step explanation:

I = P • R • T

Intrest Equals Principal Amout times Rate of Intrest times Amount of Time

P is our Principal amount of $3,000

R is our Rate of 7%

T is the time span of  years

Now if we plug in the values and solve the equation we get $3150 dollars in intrest.

Final answer:

Roxanne will earn $3,150 in interest after 15 years.

Explanation:

To calculate the interest Roxanne will earn, we can use the formula:

Interest = Principal x Rate x Time

Where Principal is the initial amount invested, Rate is the interest rate, and Time is the number of years.

Plugging in the given values, we get:

Interest = $3,000 x 0.07 x 15

Interest = $3,150

Therefore, Roxanne will earn $3,150 in interest after 15 years. This implies that Roxanne will accumulate $3,150 in interest after 15 years, illustrating the straightforward application of the interest formula to quantify the financial growth derived from the initial investment over the specified period.

Answer:

A) 75 − s = c

20s + 30c = 1,870

Step-by-step explanation:

Let us call [tex]s[/tex] the number of standard edition games and [tex]c[/tex] the number of collectors edition games.

Each standard edition game has volume of 20 in³ and each collectors edition game has volume of 30 in³, together the shipping volume is 1870 in³; therefore,

[tex]20s+30c = 1870[/tex].

Also, the company receives a total of 75 copies of the game, which means

[tex]s+c =75.[/tex]

Thus, the system of equations representing the describing the situation are

[tex]20s+30c = 1870[/tex]

[tex]s+c =75,[/tex]

which from the given choices, matches choice A. ([tex]75-s=c[/tex] can be rewritten as [tex]s+c =75[/tex])

Answer:

The answer is n < -7

Step-by-step explanation:

First, you have to move all the numbers to one side:

(-5) - (-7) > 9 + n

-5 + 7 > 9 + n

9 + n < 2

n < -7

(Hope this can help)

Answer:

the equasion of q is y=8/9x + 7/9

Step-by-step explanation:

1. to find the slope perpendicular to the slope of the first equasion, you have to find the negative recipocal, an easy way to find that is to switch the numerator and denominator of the slope as well as multiplying it by -1

2. now that you have found the slope that is perpendicular, your second equasion so far is y= 8/9x, to find the y-intercept, you plug in (7, 7) to x and y, making the equasion 7=8/9(7) + x, in this equasion x is the y intercept

3. when you solve for x for finding the y-intercept, x=7/9, which makes the equasion y=8/9x + 7/9

Answer:

y=1/4x+400

Step-by-step explanation:

Slope=Rise/Run=(300-200)/(-400-(-800))=100/400=1/4

Now we have the slope, making our equation:

y=1/4x+b

We need b, the y-intercept, which we can use any ordered pair to plug in:

200=1/4(-800)+b

200=-200+b

400=b

So the equation that passes through the points (-800, 200) and (-400, 300) is: y=1/4x+400

The equation of line that passes through the points P(-800, 200) and Q(-400, 300) is y = x/4 + 400.

The general equation of straight line is -

y = mx + c

Given is a line that passes through the points P(-800, 200) and

Q(-400, 300).

First we will find the slope of the line -

m = (y₂ - y₁)/(x₂ - x₁)

m = (300 - 200)/(-400 + 800)

m = 100/400

m = 1/4

Now, the line passes through the point Q(-400, 300). Therefore -

300 = (1/4) x (- 400) + c

300 = - 100 + c

c = 400

The final equation of the line will be -

y = x/4 + 400

Therefore, the equation of line that passes through the points P(-800, 200) and Q(-400, 300) is y = x/4 + 400.

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The other number is 375.

Step-by-step explanation:

The given information are,

The one number out of the two numbers is 300.

Let, the another number be assumed as 'x'.

The first number = 300 and the second number = x.

To find the number x :

The HCF × LCM = product of two Numbers  is a logic to used to find the unknown number.

We know the values of HCF = 75 , LCM = 1500 and one number = 300 and the second number is x.

Therefore, substituting those values in the above formula, we get

⇒ 75 × 1500 = 300 × x

⇒ 1125 / 3 = x

⇒ 375 = x

Therefore, the second number is 375.

[tex]m\angle B= 41^{\circ},[/tex] [tex]m\angle F= 70^{\circ},[/tex] [tex]m\angle H = 61^{\circ},[/tex] [tex]m\angle K= 56^{\circ}.[/tex]

Step-by-step explanation:

Step 1:

The total of the angles in any triangle is 180°.

So to determine the third angle of the given triangles, we subtract the sum of the other two sides from, 180°.

The third angle = 180° - (the first angle + the second angle).

Step 2:

For triangle ABC,

[tex]m\angle B=180^{\circ}-(\angle A+\angle C)[/tex],

[tex]m\angle B=180^{\circ}-(83^{\circ} + 56^{\circ}) = 180^{\circ} - 139^{\circ} = 41^{\circ}.[/tex]

So [tex]m\angle B= 41^{\circ}.[/tex]

For triangle DEF,

[tex]m\angle F=180^{\circ}-(\angle D+\angle E)[/tex],

[tex]m\angle F=180^{\circ}-(61^{\circ} + 49^{\circ}) = 180^{\circ} - 110^{\circ} = 70^{\circ}.[/tex]

So [tex]m\angle F= 70^{\circ}.[/tex]

Step 3:

For triangle GHI,

[tex]m\angle H=180^{\circ}-(\angle G+\angle I)[/tex],

[tex]m\angle H=180^{\circ}-(49^{\circ} + 70^{\circ}) = 180^{\circ} - 119^{\circ} = 61^{\circ}.[/tex]

So [tex]m\angle H = 61^{\circ}.[/tex]

For triangle JKL,

[tex]m\angle K=180^{\circ}-(\angle J+\angle L)[/tex],

[tex]m\angle K=180^{\circ}-(83^{\circ} + 41^{\circ}) = 180^{\circ} - 124^{\circ} = 56^{\circ}.[/tex]

So [tex]m\angle K= 56^{\circ}.[/tex]

Answer: I dont know

Step-by-step explanation:

He is almost dead and wants the pp

Answer:

The coordinates of ABCD after  the reflection across the x-axis would become:

Step-by-step explanation:

The rule of reflection implies that when we reflect a point, let say P(x, y), is reflected across the x-axis:

In other words:

The point P(x, y) after reflection across x-axis would be P'(x, -y)

P(x, y)        →       P'(x, -y)

Given the diagram, the points of the figure ABCD after the reflection across the x-axis would be as follows:

P(x, y)        →       P'(x, -y)

A(2, 3)       →       A'(2, -3)      

B(5, 5)       →       B'(5, -5)

C(7, 3)        →      C'(7, -3)

D(5, 2)       →       D'(5, -2)

Therefore, the coordinates of ABCD after  the reflection across the x-axis would become:

Answer:

36.90 = (369/10)

Radius- 5

The radius is half, so if you want to find the radius, you have to see what if half of the diameter, which is 10. So 10 divided by 2 is 5 which is the radius. Easy.

Answer:

mean: 7

median: 6

mode: no mode

Step-by-step explanation:

To find the mean, add all numbers together and subtract by how many numbers there are:

4 + 6 + 12 + 5 + 8 = 35

35/5 = 7

To find the median, you put the numbers in order from smallest to largest and find the very center number:

4, 5, 6, 8, 12

The very center number is 6

To find the mode, you choose the number that appears most often. Since every number in this set only appears once, there is no mode.

Answer:

median=6, mean=5, mode=none

Step-by-step explanation:

median= number in the middle, mean= add up all numbers then divide by how many numbers there are, mode= most common number

Answer:

Mr. Reynolds used 32 ounces of peanuts to make trail mix.

Step-by-step explanation:

One pound is equal to sixteen ounces! Simply, multiply the number of pounds by 16!

2 pounds x 16 ounces = 32 ounces

Hope this helps! :)

Answer:

NF = 16 units

Step-by-step explanation:

∵ N is the in-center of ΔABC

∴ N is equidistant from the sides AB, BC and CA

- That means the perpendicular segments from N to AB, BC

   and AC are equal

∴ ND = NE = NF

∵ ND = 6x - 2

∵ NE = 3x + 7

- Equate them to find x

∴ 6x - 2 = 3x + 7

- Subtract 3x from both sides

∴ 3x - 2 = 7

- Add 2 to both sides

∴ 3x = 9

- Divide both sides by 3

∴ x = 3

- Substitute the value of x in ND to find its length

∵ ND = 6(3) - 2 = 18 - 2

∴ ND = 16 units

∵ ND = NE = NF

∴ NF = 16 units