Gina bought 4 bags of grapes that weighed 2.29 pounds each. The grapes were priced at $2.50 per pound. The expression below represents the total cost of the bags of grapes Gina bought, in dollars.
(2.29×2.50)×4

Which expression below is also equivalent to the total cost of the grapes?


( 2.29 + 4 ) × 2.50

4 × ( 2.50 + 2.29 )

( 2.29 × 4 ) + 2.50

2.29×(2.50×4)

The surface area of the wooden structure is approximately 1012 cm².

To calculate the surface area of the wooden structure, we need to find the surface area of the cone and the surface area of the hemispherical base, and then add them together.

Surface Area of the Cone:

The surface area of a cone is given by the formula:

A_{cone = \(\pi \times r_{cone} \times (r_{cone} + s_{cone})\), \(r_{cone\) is the radius of the base of the cone and \(s_{cone\) is the slant height of the cone.

The vertical height of the cone is 24 cm, and the base radius is 7 cm, we can calculate the slant height using the Pythagorean theorem:

\(s_{cone\) = \(\sqrt{(r_{cone}^2 + h_{cone}^2).\)

Using the given measurements:

\(s_{cone\) = √(7² + 24²) cm

\(s_{cone\) ≈ √(49 + 576) cm

\(s_{cone\) ≈ √625 cm

\(s_{cone\) ≈ 25 cm

Now, we can calculate the surface area of the cone:

\(A_{cone\) = π × 7 cm × (7 cm + 25 cm)

\(A_{cone\) = (22/7) × 7 cm × 32 cm

\(A_{cone\) = 704 cm²

Surface Area of the Hemispherical Base:

The surface area of a hemisphere is given by the formula:

\(A_{hemisphere\) = \(2 \times \pi \times r_{base}^2\), \(r_{base\) is the radius of the base of the hemisphere.

Given that the base radius is 7 cm, we can calculate the surface area of the hemispherical base:

\(A_{hemisphere\) = 2 × (22/7) × (7 cm)²

\(A_{hemisphere\) = (22/7) × 2 × 49 cm²

\(A_{hemisphere\) = 308 cm²

Total Surface Area:

To calculate the total surface area, we add the surface area of the cone and the surface area of the hemispherical base:

Total Surface Area = \(A_{cone} + A_{hemisphere}\)

Total Surface Area = 704 cm² + 308 cm²

Total Surface Area = 1012 cm²

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By the SSS Congruence Theorem, △ABC ≅ △DEF.

What does a math congruent mean?

Congruent refers to having precisely the same form and size. Even after the forms have been flipped, turned, or rotated, the shape and size ought to remain constant.

What is the SSS rule?

According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle.

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-10 sin(x) = -4 csc(x) + 3

Recall that csc(x) = 1/sin(x) :

-10 sin(x) = -4/sin(x) + 3

Multiply both sides by sin(x) :

-10 sin²(x) = -4 + 3 sin(x)

Move everything to one side:

10 sin²(x) + 3 sin(x) - 4 = 0

Factorize the left side:

(2 sin(x) - 1) (5 sin(x) + 4) = 0

Then we have two cases,

2 sin(x) - 1 = 0   or   5 sin(x) + 4 = 0

Solve for sin(x) :

sin(x) = 1/2   or   sin(x) = -4/5

Solve for x :

• if sin(x) = 1/2, then

x = arcsin(1/2) + 2nπ   or   x = π - arcsin(1/2) + 2nπ

x = π/6 + 2nπ   or   x = 5π/6 + 2nπ

• if sin(x) = -4/5, then

x = arcsin(-4/5) + 2nπ   or   x = π - arcsin(-4/5) + 2nπ

x = -arcsin(4/5) + 2nπ   or   x = π + arcsin(4/5) + 2nπ

(where n is any integer)

Answer:

D. (-9,-6)

Step-by-step explanation:

Use the given slope and point to solve for y using the point-slope equation.

y-y = m(x - x)

m= 2/3  (-3, -2)

y + 2 = 2/3(x + 3)

y + 2 = 2/3x + 2

y = 2/3x

Then plug in the x's in the points that you can choose from. If the y equals the y in the given point that is the answer.

( 3,4)      y = 2/3(3) = 2

( 5,7)      y = 2/3(5) = 10/3

( -8, -4)   y = 2/3(-8) = - 16/3

( -9, -6)    y = 2/3(-9) = -6

Answer:

A. 2

Step-by-step explanation:

Point A is on the y-axis is y = -2.

-2 is 2 units away from 0, which is the y-axis.

Point B also, on the y-axis, is y = 2.

2 is also 2 units apart from the y-axis, which is y = 0.

Therefore, both points are 2 units away from the y-axis.

Answer:

it is A

Step-by-step explanation:

got it right on edge

Answer:

(C) Multiply first equation by -2 and second equation by 3, solution (1, 1)

Step-by-step explanation:

Simultaneous equations are set of equations which possess a common solution. The equations can be solved by eliminating one of the unknowns by multiplying each of the equations in a way that a common coefficient is obtained in the unknown to be eliminated.

Given the simultaneous equations:

3x - 5y = -2

2x + y = 3

First step:

Multiply first equation by -2 and multiply second equation by 3,

-6x + 10y = 4

6x + 3y = 9

Second step:

Add the two equations together,

13y = 13

Divide both sides by 13

y = 1

Third step:

Put y = 1 in the first equation

3x - 5(1) = -2

3x - 5 = -2

3x = 5 - 2

3x = 3

Divide both sides by 3:

x = 1

solution (x,y) = (1,1)

Option C

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Answer:

x= -2

x= -3

x= 5

Step-by-step explanation:

Answer:

Step 1

Step-by-step explanation:

His first error occurred in step 1.

The common denominator of \( \frac{2}{9} \) and \( \frac{1}{5} \) is 45, and not 14.

Common denominator of both fractions, is a number of which both 9 and 5 are its factor. That is, it is a common multiple of 9 and 5.

45 can be divided by 9 without remainder. Also 45 can be divide by 5 without a remainder.

45 would make both fractions common not 14.

Answer:

Option B will be your answer

Step-by-step explanation:

hope it helps

Check the picture below, the graphs of f(x) and g(x) are on the right-side.

\(\stackrel{parent}{f(x)=|x|}\qquad \qquad g(x)=\stackrel{A}{1}\left|\stackrel{B}{\frac{1}{6}}x+\stackrel{C}{0}\right|+\stackrel{D}{0}~~ \implies ~~g(x)=\left| \frac{1}{6}x \right|\)

Three- month simple moving average (sma) forecast for the average gas prices are $3.08

$3.16 , $3.29 and predict the average retail gasoline price for june 2020 is $3.54.

A simple moving average (SMA) is defined as an arithmetic moving average calculated by adding recent prices and then dividing that figure by the number of time periods in the calculation average. The formula for SMA is:

SMA = (A₁ + A₂ + ------+ Aₙ )/n

where, Aₙ = the price of object at nth period

n = the number of total periods

We have, a average gas prices for different months. Calculate the three-month moving average, add together the first three sets of data, for this example it would be Dec, January, and February. This gives a total of $9.25 , then calculate the average of this total, by dividing this figure by 3 we get 3-month simple moving average. We have to predict the 3-month simple moving average for June 2020. As we seen in above table we calculate the 3-month simple moving average for different months.

The 3-month simple moving average for June 2020 is ( $3.29 + $3.51 + $3.82 )/3 = $3.54

So, required value is $3.54..

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Complete question:

use the gas prices data below to calculate a 3-month simple moving average (sma) forecast for the average gas prices and predict the average retail gasoline price for june 2020. round your answer to two decimal places, if necessary.

Year - month Averge gas price

19-Dec $3.07

20-Jan $3.10

20-Feb $3.08

20-Mar $3.29

20-Apr $3.51

20-May $3.82

20-Jun

Step-by-step explanation:

Angle at center = 2 * Angle at circumference.

Angle MNP = 2 * Angle MQP = 30°.

Hence the angle measure of minor arc MP is 30°.

Answer:

30 degrees

Step-by-step explanation:

arc measure in degrees is twice the measure of the inscribed angle

The growth rate of the population, given the initial population and the population after 10 years is 12. 5 % every 10 years.

To find the percent change or growth rate of a quantity between two different values, you can use the formula:

Percent change = ( new value - old value ) / old value x 100%

The new value would be the population of the village after 10 years which is 450 people.

The old value is the initial population of the village which is 400

The growth rate of the population is:
= ( 450 - 400 ) / 400 x 100 %

= 12. 5 %

The growth rate for the village is therefore 12. 5 % every ten years.

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Answer: $9

Step-by-step explanation: 85% off means when you multiply the number by 0.85 you subtract that from the original number, 60 times 0.85 is 51 and 60-51=9! Hope this helps!

The growth constant is 1.0986 and the trout population will increase to 14600 after 2.1 years. The result is obtained by using the logistic equation.

The increase of population can be found by using the logistic equation. It is

\(P(t) = \frac{K}{1 + Ae^{-kt} }\)

Where

Sunset Lake is stocked with the rainbow trout. We have

Find the growth constant k and time t when P(t) = 14600!

A = (K - P₀)/P₀

A = (28000 - 2800)/2800

A = 25200/2800

A = 9

After 1 year, we have 7000 rainbow trout. The growth constant is

\(7000 = \frac{28000}{1 + 9e^{-k(1)} }\)

\(1 + 9e^{-k} = 4\)

\(9e^{-k} = 3\)

\(e^{-k} = \frac{1}{3}\)

k = - ln (1/3)

k = 1.0986

Use k value to find the time when the population will increase to 14600!

\(14600 = \frac{28000}{1 + 9e^{-1.0986t} }\)

\(1.9178 = 1 + 9e^{-1.0986t}\)

\(0.9178 = 9e^{-1.0986t}\)

\(\frac{0.9178 }{9} = e^{-1.0986t}\)

\(t = \frac{ln \: 0.10198}{-1.0986}\)

t = 2.078

t ≈ 2.1 years

It is in another 1.1 years after t = 1.

Hence, the growth constant k is 1.0986 the population will increase to 14600 when t is 2.1 years.

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Answer:

The range of scores that can earn Jeremiah a B in the course is 80 - 100

Step-by-step explanation:

Average = total scores/number of exams

For an average of 80, considering the final score has twice the weight of the previous exams;

Note: since the final score has twice the weight of previous exams, it is considered a double score and counted twice

Let the lowest final score for a B grade be y

80 = (69 + 78 + 81 + 92 + 2 * y)/6

80 * 6 = (320 + 2y)

2y = 480 - 320

y = 160/2

y = 80

Let the highest final score for a B grade be z

89 = (69 + 78 + 81 + 92 + 2 * z)/6

89 * 6 = (320 + 2z)

2z = 534 - 320

z = 214/2

z = 107

Since, the highest score in the exam cannot exceed 100,

Therefore, the range of scores that can earn Jeremiah a B in the course is 80 - 100

Answer:

E(X) = 1.9375

SD(X) = 1.20

Step-by-step explanation:

Let :

G = girl ; B = Boy

P(G) = 0.5 ; P(B) = 0.5

Sample space :

G, BG, BBG, BBBG, BBBBG, BBBBB

Using the multiplication rule of independence :

P(G) = 0.5

P(BG) = 0.5 * 0.5 = 0.25

P(BBG) = 0.5 * 0.5 * 0.5 = 0.125

P(BBBG) = 0.5 * 0.5 * 0.5 * 0.5 = 0.0625

P(BBBBG) = 0.5 * 0.5 * 0.5 * 0.5 * 0.5 = 0.03125

P(BBBBB) = 0.5 * 0.5 * 0.5 * 0.5 * 0.5 = 0.03125

Creating a probability distribution table :

X = 1, 2, 3, 4, 5

For X = 5 ;

P(BBBBG) + P(BBBBB) = 0.03125 + 0.03125 = 0.0625

X :___ 1 ____ 2 ____ 3 _____ 4 _____ 5

P(X) : 0.5 __ 0.25 _ 0.125 _0.0625 _0.0625

The expected value E(X) :

√(ΣX * P(X)) = (1*0.5)+(2*0.25)+(3*0.125)+(4*0.0625)+(5*0.0625) = 1.9375

The standard deviation SD(x) :

√(ΣX²*p(x) - E(X)²

√((1^2*0.5)+(2^2*0.25)+(3^2*0.125)+(4^2*0.0625)+(5^2*0.0625) - 1.9375^2)

√(5.1875 - 3.75390625)

√1.43359375

SD(X) = 1.197

SD(X) = 1.20

An angle is produced at the point where two or more lines meet. Thus the value of LP required in the question is approximately 14.

Two lines are said to be perpendicular when a measure of the angle between them is a right angle. While parallel lines are lines that do not meet even when extended to infinity.

From the question, let the length of LP be represented by x.

Thus, from the given question, it can be deduced that;

LM ≅ PN = 20

KP = KN - PN

    = 30 - 20

KP = 10

LP = x

Also,

<MLP is a right angle, so that;

< KLP = < KLM - <PLM

         = 126 - 90

<KLP = \(36^{o}\)

So that applying the Pythagoras theorem to triangle KLP, we have;

Tan θ = \(\frac{opposite}{adjacent}\)

Tan 36 = \(\frac{10}{x}\)

x = \(\frac{10}{Tan 36}\)

  = \(\frac{10}{0.7265}\)

x = 13.765

Therefore the side LP ≅ 14.

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Answer:

(91/3)3=9(1/3-3)=9

Step-by-step explanation:

Answer:

hows your day

Step-by-step explanation:

Answer:

16.66%

Step-by-step explanation:

7500-6250=1250

1250/7500 x 100 = 16.66%

Answer:

D. 100.5 in³

Step-by-step explanation:

We know that:

Volume of obligue cone = ⅓*area of base* height

Here

slant t=10in

height =6 in

Let's find the radius:

By using Pythagorous theorem,

slight height²=diameter²+height²

substituting value

10²=diameter²+6²

diameter²=10²-6²

diameter²=64

diameter=\(\sqrt{64}\)=8 in

Therefore, Radius= diameter/2=8/2=4 in

Now

Area of Base= πr²=π*4²=50.265

Now

Volume = ⅓*area of base*height =⅓*50.265*6=100.53 in³

So,

Volume of obligue cone is 100.5 in³

The difference between the two expressions is;

Here, we want to find the difference between the given expressions

To do this, we open up the right expression; afterwards, we bring similar terms together

Mathematically, we have this as follows;

Therefore, it would take approximately 19.02 years for an investment to at least double its original amount at a semi-annual compound interest rate of 3.62%.

When an investment is made with a certain amount, the compound interest rate is used to calculate the return on investment. In addition, the number of times interest is compounded each year can have an impact on the investment's outcome.

This question asks about how long it would take for an investment to double at a semi-annual compound interest rate of 3.62%.

To solve for how long it would take for an investment to double at a semi-annual compound interest rate of 3.62%, we need to use the formula for the future value of an annuity:

Future value of an annuity = Payment (1 + r/n)^(nt)where:r is the annual interest raten is the number of times interest is compounded per year Payment is the original amount is the number of years

To solve for t, we can rearrange the formula as follows:t = log(Payment/Future value of an annuity) / log(1 + r/n)where log is the natural logarithm.

The future value of the investment is double the original amount, so we can plug in 2 for Future value of an annuity and simplify the formula to get:t = log(2) / log(1 + 0.0362/2)t = 19.02 years

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The roots of the function F(x) = x³ + 2x² + 4x + 8 are given as follows:

B. 1 real root and 2 complex roots.

The function in this problem is defined as follows:

F(x) = x³ + 2x² + 4x + 8.

The function is of the third degree, hence the total number of zeros of the function is of 3.

From the graph, the function has only one x-intercept, which is given as follows:

x = -2.

Hence the two remaining roots are the complex roots, meaning that option B is the correct option for this problem.

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The Interest (simple interest) will be less on Loan A.

What exactly is simple interest?

Simple Interest is a simple way for computing interest on a loan or principle amount. Simple interest is a concept that is employed in numerous industries, including banking, finance, and automobiles. When you make a loan payment, the monthly interest is deducted first, followed by the principle amount.

The simple interest formula is as follows:

SI=P*R*T/100

SI stands for simple interest.

P stands for principal.

R is the interest rate (in percentage)

T denotes the length of time (in years)

The following formula is used to compute the total amount:

Amount (A) = Principal (P) x Simple Interest (SI)

Now,

For A Principal=$10000, Time = 3 years, Rate=5%

then interest paid=10000*3*5/100

=300*5=$1500

For B  Principal=$10000, Time = 5 years, Rate=8%

Interest=10000*5*8/100

=500*8

=$4000

That means SI(B)>SI(A)

Hence,  

          The Interest will be less on Loan A.

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Answer:

B two congruent pieces

Step-by-step explanation:

Perpendicular means at a 90 degree angle

bisector means it divides in it half, into two equal pieces