Mackenzie answered 72 questions correctly on her multiple choice math final that had a total of 160 problems. What percentage of questions did Mackenzie answer correctly on the final exam?

Ian earned $500 in simple annual interest after 10 years, while Jackson earned $1,128.89 more in interest than Ian after 10 years due to compound interest.

Ian's account earns simple annual interest, which means that he earns 5% interest on his initial deposit every year. After 10 years, he will have earned

interest = principal x rate x time

interest = 1000 x 0.05 x 10

interest = $500

Jackson's account earns interest that is compounded annually, which means that he earns 5% interest on his initial deposit plus any interest that has already been earned every year. After 10 years, he will have earned

[tex]balance = principal x (1 + rate)^{time}[/tex]

balance = 1000 x (1 + 0.05)¹⁰

balance = $1,628.89

To find out how much more interest Jackson earned than Ian, we need to subtract the interest Ian earned from the balance in Jackson's account

$1,628.89 - $500 = $1,128.89

Therefore, Jackson earned $1,128.89 more in interest than Ian after 10 years.

To know more about interest:

https://brainly.com/question/15089941

#SPJ1

The requreid, as per the given percentage condition Mia tips the movers $80.

To find the amount of the tip, we need to calculate 16% of the total cost of the services, which is $500.

16% of $500 = 0.16 x $500 = $80

Therefore, Mia tips the movers $80.

Learn more about percentages here;

https://brainly.com/question/11642000

#SPJ1

Answer:

125

Step-by-step explanation:

50 refrigerators are 40% of all the refrigerators in the store.

5 refrigerators are 4% of refrigerators in the store

125 refrigerators are 100% of refrigerators in the store

therefore there are 125 refrigerators at the store.

Answer:

To translate triangle ABC 3 units up, we need to add 3 to the y-coordinate of each vertex:

A = (-3, 3 + 3) = (-3, 6)

B = (0, 7 + 3) = (0, 10)

C = (-3, 0 + 3) = (-3, 3)

Therefore, the coordinates of the vertices for the image triangle A'B'C' are A(-3, 6), B'(0, 10), and C(-3, 3).

So the correct answer is: A(−3, 6), B(0, 10), C(−3, 3).

6 inches will be the length of the patio.

According to the scale, 1 inch on the plan corresponds to 3.5 feet in real life.

We must convert the patio's real length of 21 feet to inches using the scale in order to determine how long it would look on the blueprint:

3.5 feet to one inch

21 feet in x inches

If we cross-multiply, we obtain:

1 inch/3.5 feet * 21 feet

= x inches

= 6 inches.

As a result, the length of the patio will be indicated on the blueprint as 6 inches.

Learn more about scale here:

https://brainly.com/question/30468792

#SPJ1

The two numbers given by the algebraic expressions are x = 5 and y = 2.

A system of equations is a set of two or more equations that are to be solved simultaneously. In other words, a system of equations represents multiple relationships between variables that need to be solved for at the same time. A system of equations can be solved using various methods, such as substitution or elimination. The goal of solving a system of equations is to find the values of the variables that satisfy all of the equations in the system. One common method for solving systems of linear equations is called Gaussian elimination, which involves manipulating the equations in the system to eliminate one variable at a time until a solution is found.

Let us suppose the numbers as x and y.

From the given statement the mathematical expression can be set as:

y = 2x - 8

x + y = 7

Now. substituting the value of y in equation we have:

x + (2x - 8) = 7

3x - 8 = 7

3x = 15

x = 5

Now, for x = 5 the value of y is:

y = 2(5) - 8

y = 2

Hence, the two numbers are x = 5 and y = 2.

Learn more about system of equations here:

https://brainly.com/question/24065247

#SPJ1

The complete question is:

The number y is 8 less than 2 times another number x, their sum is 7. Find the number.

The supplied value of 4 is a solution to the equation m + 2(m + 1) = 14.

Given the equation in the question;

m + 2(m + 1) = 14

And supplied value = 4

To substitute the value of 4 into the equation, we replace every occurrence of the variable "m" with 4:

m + 2(m + 1) = 14

Plug in m = 4 by replace m with 4 and simplify both sides

4 + 2(4 + 1) = 14

4 + 2(5) = 14

4 + 10 = 14

14 = 14

We can see that both sides of the equation simplify to 14, which means that the value of 4 is a solution.

Learn more about equations here: https://brainly.com/question/9236233

#SPJ1

Answer:

1/2 page per second

Step-by-step explanation:

5/10 ÷ 10/10 = .5/1 = .5 or 1/2 page per second.

Helping in the name of Jesus.

Tje number of items in the ratio 8:27, proportioned according to the total number of items sent (1225), is 280 items in the 8 part and 945 items in the 27 part.

To find out how many items there are in 1 part of the ratio, we need to add together the two parts of the ratio. In this case, 8+27 = 35.

To proportion the items according to the ratio, we need to divide the total number of items (1225) by the number of parts in the ratio (35).

This gives us:

1 part of the ratio = 1225 / 35 = 35

To find out how many items there are in each part of the ratio, we need to multiply this value by the corresponding part of the ratio.

For the part that corresponds to 8, we have:

8 parts of the ratio = 8 x 35 = 280 items

For the part that corresponds to 27, we have:

27 parts of the ratio = 27 x 35 = 945 items

Therefore, the number of items in the ratio 8:27, proportioned according to the total number of items sent (1225), is 280 items in the 8 part and 945 items in the 27 part.

Learn more about ratio on

https://brainly.com/question/12024093

#SPJ1

Answer:

x = 67.4°

y = 22.6°

Step-by-step explanation:

The tangent ratio is a trigonometric ratio that relates the ratio of the length of the side opposite an angle in a right triangle to the length of the side adjacent to that angle.

[tex]\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}[/tex]

The side opposite angle x is 7.2, and the side adjacent angle x is 3.

Use the tangent trigonometric ratio to find the measure of angle x:

[tex]\begin{aligned}\tan(x)&=\dfrac{7.2}{3}\\x&=\tan^{-1}\left(\dfrac{7.2}{3}\right)\\x&=\vphantom{\dfrac12}67.380135...^{\circ}\\x&=67.4^{\circ}\;\sf (nearest\;tenth)\end{aligned}[/tex]

Therefore, x = 67.4°.

The side opposite angle y is 3, and the side adjacent angle y is 7.2.

Use the tangent trigonometric ratio to find the measure of angle y:

[tex]\begin{aligned}\tan(y)&=\dfrac{3}{7.2}\\y&=\tan^{-1}\left(\dfrac{3}{7.2}\right)\\y&=\vphantom{\dfrac12}22.6198649...^{\circ}\\y&=22.6^{\circ}\;\sf (nearest\;tenth)\end{aligned}[/tex]

Therefore, y = 22.6°.

The value of x when the secant intersect is 5.

When two secants intersect outside a circle, the circle divides the secants into segments that are proportional with each other.

Therefore,

(4 + 5)4 = (x - 2 + x + 4)(x - 2)

9(4) = (2x + 2)(x - 2)

36 = 2x² - 4x + 2x - 4

2x² - 2x - 4 - 36 = 0

2x² - 2x - 40 = 0

x² - x - 20 = 0

x² - 5x + 4x  - 20 = 0

x(x - 5) + 4(x - 5) = 0

(x + 4)(x - 5) = 0

(x - 5)(x + 4) = 0

x = 5 or x = -4

Therefore,

x = 5

learn more on secant here: https://brainly.com/question/23026602

#SPJ1

Therefore , the solution of the given problem of probability comes out to be  z-score from a typical normal distribution.

Any considerations technique's fundamental objective is to determine the likelihood that a claim is true or that a particular incident will take place. Any number range from one to one, when 0 traditionally signifies a percentage and 1 typically implies the degree of certainty, can be used to represent chance. A probability illustration shows the likelihood that a particular event will occur.

Here,

The formula for the standard error of the mean (SEM), which is as follows:

=> SEM = the standard deviation / √(sample size).

We can enter these numbers into the SEM calculation to determine the SEM given that the standard deviation of the tariff rates is $1200 and the sample size is 400:

=> SEM=$1200/√(400)

=> $1200/20 =$60

It is possible to calculate the z-score for a $80 departure from the mean with a $60 SEM as follows:

=>  z = (80 - 0) / $60 = 1.3333

Now that we have the probability corresponding to the z-score of 1.3333,

we can look up the cumulative distribution function (CDF) of the standard normal distribution using a z-table or a statistical calculator.

The CDF depicts the likelihood that a random variable will occur is less than or equal to a certain z-score from a typical normal distribution.

To know more about probability visit:

https://brainly.com/question/11234923

#SPJ1

The two solutions to the simultaneous equations are; y1 = -0.87  and y2 = 2.87. x1 = 2.87, x2 =  -0.87

To solve these simultaneous equations, we can use the method of substitution. We can rearrange the second equation to isolate one of the variables, for example, y:

y = 2 - x

Now, substitute this expression for y into the first equation:

x^2 + (2 - x)^2 = 9

Expand the equation:

x^2 + (4 - 4x + x^2) = 9

Combine like terms:

2x^2 - 4x + 4 = 9

Move all terms to one side to set the equation to equal zero:

2x^2 - 4x - 5 = 0

Now, we can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In our equation, a = 2, b = -4, and c = -5:

x = (4 ± √((-4)^2 - 4(2)(-5))) / (2 x 2)

x = (4 ± √(16 + 40)) / 4

x = (4 ± √56) / 4

The two possible values for x are:

x1 ≈ (4 + 7.48) / 4 = 2.87

x2 ≈ (4 - 7.48) / 4 = -0.87

Now, we'll find the corresponding y values using the equation y = 2 - x:

For x1 ≈ 2.87:

y1 ≈ 2 - 2.87 ≈ -0.87

For x2 ≈ -0.87:

y2 ≈ 2 - (-0.87) ≈ 2.87

So, the two solutions to the simultaneous equations are approximately (2.87, -0.87) and (-0.87, 2.87), both correct to 2 decimal places.

Find more exercises on simultaneous equations;

https://brainly.com/question/16763389

#SPJ1

Answer:

142 ft square

Step-by-step explanation:

Face 1: 3(10)=30 ft square

Face 2: 4(10)=40 ft square

Front: 2(6)=12/2=6 ft square

Back: Same as front

bottom: 6(10)=60 ft square

Total: 30+40+6(2)+60=142 ft square

() means multiply in case don't know

Note that the angles are found using the principle of the circle theorems.

The angle of the circumference is half of the angle at the center of the circle by an arc.

AB = 78°

∠5 = 39°

Angles intercepted by the same arc are equal.

∠4 = 39°

FE= 105°

∠16 =105°

ED = 27°

∠17 =27°

CD = 42°

∠10 =21°

∠3 =21°

The angle of the semi-circle is 90°.

∠2 =90°

∠8=∠9 = (180-48)/2

∠8= 66°

∠9= 66°

∠7=90°-∠8 = 90°-66°

∠7=24°

∠17 = 180°-∠15-∠16

∠17 = 180°-48°-105°

∠17 =27°

∠6=∠15/2 = 48/2

∠6=24°

∠21 = 180°-∠7-∠16

∠21 = 180°-24°-105°

∠21 =51°

∠19 =51°

∠18 = 180°-∠17-∠6

∠18 = 180°-27°-24°

∠18 = 129°

∠20 = 129°

BC = 60°

∠1 = 60/2

∠1 =30°

∠11=180°-∠1-∠2

∠11=180°-30°-90°

∠11=60°

∠13=60°

∠12=180-∠11

∠12=180°-60°

∠12=120°

∠14=120°

∠15=48°

Learn more about circle theorem:
https://brainly.com/question/31703930
#SPJ1

The number of triangles that are displayed can be found to be 216 triangles.

Each rectangular tile has a decorative pattern of 3 equal-sized squares, and each square is divided into 2 same-sized triangles. Therefore, each tile has 3 squares * 2 triangles per square = 6 triangles.

Marnie uses 36 of these tiles on the wall behind her kitchen stove. To find the total number of triangles displayed, multiply the number of triangles per tile by the total number of tiles:

Total triangles = 6 triangles per tile x 36 tiles = 216 triangles

So, there are 216 triangles displayed on the wall behind Marnie's kitchen stove.

Find out more on triangles at https://brainly.com/question/17488511

#SPJ1

With this strategy, the ball will travel approximately 28.98 meters horizontally before it hits the ground.

To solve this problem, we will need to find the time of flight and the horizontal velocity. We can use the following kinematic equations:

Vertical motion:

Maximum height: h = (v^2 * sin^2(angle)) / (2 * g)

Time of flight: t = 2 * v * sin(angle) / g

Horizontal motion:

Range: R = v * t * cos(angle)

Given:

Initial velocity (v) = 20 m/s

Angle = 45 degrees

Acceleration due to gravity (g) = 9.81 m/s²

Calculations:

Convert angle to radians: 45 degrees = 45 * (π/180) = 0.785 radians

Calculate time of flight: t = 2 * 20 * sin(0.785) / 9.81 = 2.04 seconds

Calculate horizontal range: R = 20 * 2.04 * cos(0.785) = 28.98 meters

So, with this strategy, the ball will travel approximately 28.98 meters horizontally before it hits the ground.

Read more about Vertical motion here:

https://brainly.com/question/24230984

#SPJ1

A ball is thrown with an initial velocity of 20 meters per second at an angle of 45 degrees with respect to the horizontal. How far does the ball travel horizontally (range) before it hits the ground? Assume no air resistance.

Answer:

G(x) = (x - 2)^2 + 1, so A is correct.

Step-by-step explanation:

you remember the priorities of mathematical operations :

1. brackets

2. exponents

3. multiplications and divisions

4. additions and subtractions

it is irrelevant how close or how far apart the operands are written.

I think, missing operators are multiplications.

so, by writing really everything

(7 × 6) ÷ 2 × [{45 + 3 × (7 × 2 - 15 + 6)} + 4]

we get in a first step :

(42) ÷ 2 × [{45 + 3 × (14 - 15 + 6)} + 4]

second step

21 × [{45 + 3 × (5)} + 4]

third step

21 × [{45 + 15} + 4]

fourth step

21 × [60 + 4]

fifth step

21 × 64

sixth step

1,344

Answer: To find the area of a triangle, we can use the formula:

Area = (base x height) / 2

However, in this problem, we don't have the height of the triangle directly. Instead, we have the lengths of three sides of the triangle.

To find the height, we can use Heron's formula, which allows us to calculate the area of a triangle when we know the lengths of all three sides:

Area = √(s(s-a)(s-b)(s-c))

where a, b, and c are the lengths of the sides of the triangle, and s is the semi-perimeter (half of the perimeter) of the triangle:

s = (a + b + c) / 2

Once we have the area of the triangle, we can use the given price per square foot to calculate the cost of the lot.

So, to apply this to the problem at hand, we can first calculate the semi-perimeter of the triangle:

s = (94 + 188 + 168) / 2 = 250

Next, we can use Heron's formula to find the area of the triangle:

Area = √(250(250-94)(250-188)(250-168)) ≈ 7329.53 square feet

Finally, we can calculate the cost of the lot by multiplying the area by the price per square foot:

Cost = 7329.53 x $3 = $21,988.59

Therefore, the approximate cost of the triangular lot is $21,988.59.

Step-by-step explanation:

The surface area is 653.1 square centimeters.

What is surface area?

A three-dimensional object's surface area is the space it takes up when viewed from the outside.

Here the given inner cylinder diameter d = 7m then

Radius r= d/2 = 7/2 = 3.5m

Now outer cylinder diameter = 9 cm then

Radius R= d/2 = 9/2 = 4.5 cm.

Height h = 26 cm.

Now using surface area of cylinder formula then,

=> Surface area A = [tex]\pi (R^2-r^2)h[/tex] square unit.

=> A = [tex]3.14(4.5^2-1.5^2)26[/tex]

=> A = [tex]3.14\times(20.25-12.25)\times26[/tex]

=> A = 3.14×8×26

=> A = 653.1 square centimeters.

Hence the surface area is 653.1 square centimeters.

To learn more about surface area refer the below link

https://brainly.com/question/16519513

#SPJ1

The perimeter of a square is the sum of its sides and they are all equal, so to obtain the length of each of them we divide the perimeter of the first fence between 4:

[tex]\text{P1}= \dfrac{\text{64 feet}}{\text{4 sides}}[/tex]

[tex]\text{P1}= 16 \ \text{feet}[/tex]

Then, the length of each side of the second fence will increase 2 feet at each end, as shown in the figure. We have then that the perimeter of the second fence is:

[tex]\text{P2 = 20 feet} \times \text{4 sides}[/tex]

[tex]\text{P2 = 80 feet}[/tex]

The sum of the perimeters of both fences is:

[tex]\text{PT = P1 + P2}[/tex]

[tex]\text{PT = 64 feet + 80 feet}[/tex]

[tex]\text{PT = 144 feet}[/tex]

Total cost = $1.26 x 144 feet

Total cost = $181.44

The total cost of the fences was $181.44

The amount that Marcus will receive when he redeems the CD at the end of the 19 years, which is described as the compounded future value, is $37,255.14.

The future value is the present investment or value compounded at an interest rate.

The future value can be determined using the FV formula or an online finance calculator as follows:

N (# of periods) = 228 months (19 years x 12)

I/Y (Interest per year) = 7.5%

PV (Present Value) = $9,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $37,255.14

Total Interest: $28,255.14

Learn more about determining the future values at https://brainly.com/question/24703884.

#SPJ1

The sum of the two complex numbers is 9 - √30) + 2√(5)i.

Explain complex numbers

Complex numbers are numbers that consist of a real part and an imaginary part, expressed as a+bi, where a and b are real numbers and i is the imaginary unit. They are used in mathematics to represent solutions to equations that cannot be solved using only real numbers.

According to the given information

To add complex numbers (4+√(-20i)) and (5+√(-30i)), we add their real parts separately and their imaginary parts separately:

Real parts: 4 + 5 = 9

Imaginary parts: √(-20i) + √(-30i)

We can simplify each of the square roots using the fact that:

√(-1) = i

Therefore:

√(-20i) = √(20) * √(i) = 2√(5) * i

√(-30i) = √(30) * √(i) = √30) * i * √(-1) = √(30) * i^2 = -√(30)

So the imaginary parts simplify to:

2√(5)i - √(30)

Putting it all together, we get:

(4+√(-20i)) + (5+√(-30i)) = 9 + (2√(5)i - √(30)) = 9 - √(30) + 2√(5)i

Therefore, the sum of the two complex numbers is 9 - √(30) + 2√(5)i.

To know more about complex numbers visit

brainly.com/question/20566728

#SPJ1

The best response to Raina's comment will be that technology is good but handouts still serve the useful purpose of being a hard copy that speakers can use in case technology fails.

To respond to Raina, the best thing to do will be to acknowledge the fact that technology is good but handouts are still important because, unlike technology that can trip off by some sudden technical faults, handouts can be depended upon.

So, while responding to Raina, we will not discard her point but will let her know that technology is good but handouts still have their benefits.

Learn more about technology and handouts here:

https://brainly.com/question/14995912

#SPJ1

The surface area of the prism is 426 m²

A cuboid is a rectangular prism. And has all the properties related to a prism. The general formula for the surface area of a cuboid is ;

SA = 2B + ph

We can use net formula to find the surface area of a cuboid.

surface area of a cuboid is expressed as;

SA = 2( lb+lh +bh)

l = 12m , b = 5m and h = 9m

lb = 12×5 = 60m²

lh = 12 × 9 = 108m²

bh = 5×9 = 45m²

SA = 2(60+108+45)

= 2(213)

= 426 m²

therefore the surface area of the cuboid is 426m²

learn more about surface area of cuboid from

https://brainly.com/question/20919556

#SPJ1

Answer:

176

Step-by-step explanation:

To do this question, we can simplify it even further.

If x=25 when y=110, it is in the ratio 25:110.

If we divide by five on both sides, the ratio becomes:

5:22.

Then, if we multiply by eight on both sides,

it becomes 40:22x8 which means y is equal to 176.

Answer:

Step-by-step explanation:

(3n³ + 2n)² = 9n^6 + 12n^4 + 4n^2

(4k² + 2k³) = 2k²(2 + k)

(3y²-y')' = 6y-y''

(4c+30) = 2(2c+15)

(2b² * b)² = 4b^6

(2gh²)* = 2gh^2

(6w³)² = 36w^6

Answer:

Step-by-step explanation:

On solving the question, we can say that Therefore, none of the answers to the question's assertions are true.

A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.

Let's use "x" to symbolise box A's weight. Then, we could type:

Given that box B weighs 5 kg more than box A, its weight is "x + 5".

Given that box C weighs 3 kg more than box B, its weight is calculated as "x + 5 + 3" = "x + 8".

We can write: Since we are aware that the combined weight of the three boxes is 51 kg:

[tex]x + (x + 5) + (x + 8) = 51\\3x + 13 = 51\\3x = 38\\x = 12.67\\[/tex]

Therefore, box A weights around 12.67 kg. The weights of boxes B and C may also be ascertained using the equations we discovered earlier:

17.67 kg (x + 5) is the estimated weight of Box B.

The approximate weight of Box C is 25.67 kg (x + 8).

Therefore, none of the answers to the question's assertions are true.

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1