Mr frank bought 6 pounds of grapes and 3 pounds of apples in the store. he paid $28.20 for the whole purchase. his neighbor mrs. bland pain $16.90 for 2 pounds of grapes and 4 pounds of apples. if all of the apples in the store cost the same and all grapes cost the same, what is the price of one pound of grapes?

Answers

Answer 1

The price of one pound of grapes and one pounds of apples in the store is $3.45 and $2.5 respectively.

Simultaneous equation

let

x = price of grapesy = price of apples

6x + 3y = 28.20

2x + 4y = 16.90

multiply equation (2) by 3

6x + 3y = 28.20

6x + 12y = 50.70

subtract the equation

9y = 22.50

y = 22.50/9

y = $2.5

substitute y into (2) in

2x + 4y = 16.90

2x + 4(2.5) = 16.90

2x + 10 = 16.90

2x = 16.90 - 10

2x = 6.90

x = 6.90/2

x = $3.45

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Related Questions

52% of students in a class have brown hair. If 4 students are chosen at random, what is the probability that exactly 3 have brown hair? Write your answer in percent rounded to the nearest whole number.​

Answers

Answer:

[tex]P(X=3)\approx27\%[/tex]

Step-by-step explanation:

Use the binomial distribution

[tex]\displaystyle P(X=k)=\binom{n}{k}p^k(1-p)^{n-k}\\\\P(X=3)=\binom{4}{3}(0.52)^3(1-0.52)^{4-3}\\\\P(X=3)=\frac{4!}{3!(4-3)!}(0.52)^3(0.48)^1\\ \\P(X=3)=0.26996736\\\\P(X=3)\approx0.27\\\\P(X=3)\approx27\%[/tex]

Therefore, the probability that exactly 3 students out of 4 randomly chosen students have brown hair is about 27%

Look at this set of 5 numbers: 21471 By how much would the mode decrease if the number 1 were added to the set?

Answers

Answer:

Zero

Step-by-step explanation:

The mode is the number of most repeated data in the set.

Given set 2, 1, 4, 7, 1 has mode 1 (repeated twice).

If we add 1 to the set the mode will remain 1 as it will repeat three times, so the mode won't change.

There is no change in mode, so the mode decrease is zero.

Answer:

The mode would not decrease

Step-by-step explanation:

Given set of numbers:  2, 1, 4, 7, 1

The mode is most frequently occurring data value.

Therefore, 1 is the mode of the given data set as there are two of this data value.

If we add 1 to the data set, the set becomes:  2, 1, 4, 7, 1, 1

Therefore, 1 is still the mode since there are now three of this data value.

In conclusion, the mode would stay the same.

The mechanic does 6 oil changes 2 hours. How many oil changes can the mechanic do in 8 hours?

Answers

Answer:

24

Step-by-step explanation:

6/2 = x/8

x=24

24 oil changes

A particle moves on the circle x2 y2=25 in the xy-plane for time t≥0. At the time when the particle is at the point (3,4), dxdt=6. What is the value of dydt at this time?

Answers

The movement of the particle on the circle is its displacement.

The value of dy/dt at this time is -9/2.

What is the differentiation?

Differentiation is a process, in Maths, where we find the instantaneous rate of change in function based on one of its variables.

A particle moves on the circle x^2 + y^2=25 in the XY-plane for time t≥0. At the time when the particle is at the point (3,4), dxdt=6.

The equation of the circle is given as:

[tex]\rm x^2 + y^2=25[/tex]

Differentiate with respect to time

[tex]\rm 2x \times \dfrac{dx}{dt}+2y \times \dfrac{dy}{dt}=0[/tex]

Substitute all the values in the equation

[tex]\rm 2x \times \dfrac{dx}{dt}+2y \times \dfrac{dy}{dt}=0\\\\2(3) \times 6+2(4)\times \dfrac{dy}{dt}=0\\\\ 6 \times 6+8 \times \dfrac{dy}{dt}=0\\\\ 36+8\times \dfrac{dy}{dt}=0\\\\ 8\times \dfrac{dy}{dt}=-36\\\\ \dfrac{dy}{dt}= \dfrac{-36}{8}\\\\ \dfrac{dy}{dt}= \dfrac{-9}{2}[/tex]

Hence, the value of dy/dt at this time is -9/2.

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if f(c)=2x^2-x, find f(-4) - f(9)

Answers

Answer:

-13f

Simplify by combining the sum of 4 + 9 with the term "f" and assume integers will be negative.

i will mark brainliest!

Answers

The completed code to generate and save a number in the program which allow a user to guess a number from (1,10) is input.

What is a program in coding?

Program or programming is the combination of codes. These codes are used to generate the program such that a machine can understand the inputs given to it.

The program is written to allow a user to guess a number. This number should be between the number 0 to 10.

Here, the input is needed to a machine or computer, for which it's process the number and show if the guessed number is correct or not.

Hence, the completed code to generate and save a number in the program which allow a user to guess a number from (1,10) is input.

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To convert
Convert 0.75 liter to milliliters.
Enter your answer in the box.
mL

Answers

Answer:

750 mL

Step-by-step explanation:

Unit Conversion Rate

1 Liter (L) = 1000 Milliliters (mL)

Solving

1 x 0.75 L = 1000 x 0.75 mL0.75 L = 750 mL

Answer:

750

Step-by-step explanation:

.75 x 1000 = 750

multiply volume value by 1000

hope this helps!

Please help me on this!

Answers

The positive integer for which g(x) first exceeds f(x) is 178 according to the number line.

What is the function of f(x)?

The function f of (x) is used to denote a linear algebra that can be represented on the graph.

Given that:

f(x) = 2x + 15[tex]\mathbf{g(x) = 11(1.02)^x}[/tex]

We are to determine a positive integer for which g(x) first exceeds f(x). Using the following option;

f(x) = 2(371) + 15 = 757g(x) = 11(1.02)³⁷¹  = 17063.04

f(x) = 2(177) + 15 = 369g(x) = 11(1.02)¹⁷⁷  = 366.11

f(x) = 2(370) + 15 = 755g(x) = 11(1.02)³⁷⁰ = 16728.47

f(x) = 2(178) + 15 = 371g(x) = 11(1.02)¹⁷⁸ = 373

Therefore, we can conclude that the positive integer for which g(x) first exceeds f(x) is 178 according to the number line.

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Find the area of the following region. The region outside the circle r=3 and inside the circle r=-6cos theta

Answers

The region outside the circle r = 3 and inside the circle r = - 6cos θ is given below.

[tex]\rm Area = \dfrac{12\pi - 9\sqrt3 }{2}[/tex]

What is an area bounded by the curve?

When the two curves intersect then they bound the region is known as the area bounded by the curve.

The region outside the circle r = 3 and inside the circle r = - 6cos θ

Then the value of the θ will be

[tex]\begin{aligned} -6\cos \theta &= 3\\\\\cos \theta &= -\dfrac{1}{2}\\\\\theta &= -\dfrac{2\pi}{3}, \dfrac{2\pi}{3} \end{aligned}[/tex]

Then the area will be given as

[tex]\rm Area = \dfrac{1}{2} \int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}} [-6 \cos \theta)^2 - 3^2 ] d \theta \\\\\\Area = \dfrac{1}{2} \int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}} [18 (2\cos ^2 \theta ) - 9]d \theta \\\\\\Area = \dfrac{9}{2} \int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}} [2(1 + \cos 2\theta ) - 1] d \theta \\\\\\Area = \dfrac{9}{2} \int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}} [2 \cos 2\theta ) + 1] d \theta \\\\[/tex]

[tex]\rm Area = \dfrac{9}{2} [ \sin 2\theta + \theta ] _{-\frac{2\pi}{3}}^{\frac{2\pi}{3}} \\\\\\ Area = \dfrac{9}{2} [ \sin 2( \frac{2\pi}{3}) +\frac{2\pi}{3} - \sin 2 (\frac{2\pi}{3}) - \frac{2\pi}{3}] \\\\\\[/tex]

On simplifying, we have

[tex]\rm Area = \dfrac{12\pi - 9\sqrt3 }{2}[/tex]

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is 14/4 rational or irrational

Answers

Answer:

Rational

Step-by-step explanation:

All fractions are rational numbers but it is not necessary that all rational numbers are fractions.

Have a nice day! :)

Kim projects an image using a ratio
of image measurements to projection
measurements of 2:9. A car in the
image has a width of 0.2 meter. Find
the width of the car in the projection.
x represents the
y represents the
Equation:
The width
projection is
the car in the
meter.

Answers

Answer:

= 0,16m

Step-by-step explanation:

we are given the ratio there the 2 is for the image 9 is for the car so we say 9 divide by 11 multiply by 0,2

Scores on a recent administration of the SAT were approximately normally
distributed with a mean of 980 and a standard deviation of 135. Between what 2
scores would you expect to find about 95% of all test-takers?
Blank #1
Blank #2

Answers

Answer:

25 to 3 power ÷ 3 = 69

HELPPP!!!!

Solve this system of equations using the inverse of a matrix.
-x +y = 8
4x + 3y = 12
x - 7y + z = 15

Answers

The Solution of -x +y = 84, x + 3y = 12, x - 7y + z = 15 be [tex]\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; =\left[\begin{array}{ccc}-1.76\\6.24\\60.76\end{array}\right][/tex]

The correct option is (C)

What is inverse of Matrix?

The inverse of matrix is another matrix, which on multiplying with the given matrix gives the multiplicative identity.

Given equation are:

-x +y = 8

4x + 3y = 12

x - 7y + z = 15

So,

[tex]\left[\begin{array}{ccc}-1&1&0\\4&3&0\\1&-7&1\end{array}\right] \;*\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; = \; \left[\begin{array}{ccc}8\\12\\15\end{array}\right][/tex]

then,

[tex]\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; = \; \left[\begin{array}{ccc}-1&1&0\\4&3&0\\1&-7&1\end{array}\right]^{-1} \; \left[\begin{array}{ccc}8\\12\\15\end{array}\right][/tex]

Now, Calculating the inverse of Matrix we have,

[tex]\left[\begin{array}{ccc}-1&1&0\\4&3&0\\1&-7&1\end{array}\right]^{-1} \;[/tex] =      [tex]\left[\begin{array}{ccc}-3/7&1/7&0\\4/7&1/7&0\\31/7&6/7&1\end{array}\right][/tex]

so, [tex]\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; = \;\left[\begin{array}{ccc}-3/7&1/7&0\\4/7&1/7&0\\31/7&6/7&1\end{array}\right]\; \left[\begin{array}{ccc}8\\12\\15\end{array}\right][/tex]

 

[tex]\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; =\left[\begin{array}{ccc}-12/7\\44/7\\425/7\end{array}\right][/tex]

 [tex]\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; =\left[\begin{array}{ccc}-1.76\\6.24\\60.76\end{array}\right][/tex]

Hence ,[tex]\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; =\left[\begin{array}{ccc}-1.76\\6.24\\60.76\end{array}\right][/tex]

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are all natural numbers also an integer? (yes/no) [math 2+]

Answers

Yes because every natural number is a whole number because integers are those numbers which are starts from 0 to infinity positive and negative and natural numbers are those numbers which are starts from 1 to infinite positive numbers. Natural numbers are all positive integers.

You are given a vector in the xy plane that has a magnitude of 87. 0 units and a y component of -66. 0 units. Determine the direction of a vector

Answers

You are given a vector in the XY plane that has a magnitude of 87. 0 units and a y component of -66. 0 units. The direction of the vector V is;

How to know the direction of a vector?

We know that the formula for 2 vectors like this in the x and y directions is; A = xi^ + yj^

Where A is the magnitude of the resultant

x is the value of the x-component

y is the value of the y-component

We are given;

Magnitude of vector = 84 units

Y-component of the vector = -67 units

Thus,

[tex]A = \sqrt(x^2 + y^2)\\\\87 = \sqrt(x^2+ (-66)^2)\\\\87^2= x^2+ 4356\\\\7569 = x^2+ 4356\\\\x= \sqrt(7569 - 4356)\\\\x = 56.68 units[/tex]

From A above, let us take the positive value of the x-component and as such our original vector will be;

A = 56.68i^ - 66j^

The direction of the vector V is;

[tex]\theta = tan^{-1} \dfrac{y}{x} \\\\\theta = tan^{-1} \dfrac{-66}{56.68} \\\theta =-27.15°[/tex]

Since it points entirely to the negative x-axis, then the angle is;

180 - (-27.15) = 207.15°

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PLEASE HELPPP
The function f is giving by
f(x) = (x - 2)(x +4). What are the x-intercepts of the graph representing f?

Answers

PLEASE HELPPP
The function f is giving by
f(x) = (x - 2)(x +4). What are the x-intercepts of the graph representing f?

Answer:

X intercepts are (-4,0) and (2,0)

Step-by-step explanation:

use the desmos graphing calculator for a simple answer

What is 3 3/4 x = 1 1/4

Answers

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

1. Convert both mixed numbers into improper fractions:

[tex]\frac{15}{4} x = \frac{5}{4}[/tex]

2. Multiply both sides by 4:

4 · [tex]\frac{15}{4} x=\frac{5}{4}[/tex] · 4

15x = 5

3. Isolate x:

x = 1/3

hope this helps!

An article sells for $415. 80. You wish to discount it by 20%. At what price will you offer it after the discount?

Answers

Answer:

$332.64

Step-by-step explanation:

Since we are applying a discount to a price tag, we will be decreasing the amount of that price tag.

In this case, we will be taking 20% off of $415.80. This means that our new price tag will be 80% of what it originally was. To find the answer, we must first change 80% into a decimal.

80% ->  [tex]\frac{80}{100}[/tex] -> 0.980

Next, we multiple $415.80 by 0.80 as shown below:

[tex]415.80(0.80)[/tex]

Our answer will be:

$332.64

I need help on 11A, I got the answer as 5.046cm but the book says it's 8.37 cm

Answers

Answer:

[tex]\textsf{Area of a triangle}=\dfrac{1}{2} ab \sin C[/tex]

(where [tex]a[/tex] and [tex]b[/tex] are the sides, and [tex]C[/tex] is the included angle)

[tex]\textsf{Area of a sector}= \dfrac{\theta}{360} \pi r^2[/tex]

(where [tex]\theta[/tex] is the angle in degrees and [tex]r[/tex] is the radius)

Therefore, using the above formulas:

[tex]\begin{aligned}\textsf{Area of segment } \rm (A) & = \textsf{area of sector}- \textsf{area of triangle}\\& = \dfrac{\theta}{360} \pi r^2 - \dfrac{1}{2}r^2 \sin \theta\\\end{aligned}[/tex]

Given:

[tex]\theta[/tex] = 90°A = 20 cm²

Substitute the given values into the formula and solve for r:

[tex]\begin{aligned}\implies 20 & = \dfrac{90}{360} \pi r^2 - \dfrac{1}{2}r^2 \sin 90\\\\20 & = \dfrac{1}{4} \pi r^2 - \dfrac{1}{2}r^2 (1)\\\\20 & = \left(\dfrac{1}{4} \pi -\dfrac{1}{2}\right)r^2\\\\20 & = \left(\dfrac{\pi -2}{4}\right)r^2\\\\r^2 & = 20\left(\dfrac{4}{\pi -2}\right)\\\\r^2 & =\dfrac{80}{\pi-2}\\\\r & =\sqrt{\dfrac{80}{\pi-2}}\\\\r & = 8.37\: \sf (2\:dp)\end{aligned}[/tex]

Part A: Explain why x = 6 makes 4x − 5 ≤ 19 true but not 4x − 5 < 19. (5 points)

Part B: What value from the set {4, 5, 6, 7, 8} makes the equation 4x + 3 = 23 true? Show your work. (5 points)

Answers

This solution shows that 6 is included in the solution due to the equal sign and not true for the inequality  4x − 5 < 19 since 6 is excluded

Inequality expression

Inequalities are equation not separated by an equal sign

Given the inequality expression

4x − 5 ≤ 19

4x ≤ 19 + 5

4x ≤  24

x≤ 6

This solution shows that 6 is included in the solution due to the equal sign and not true for the inequality  4x − 5 < 19 since 6 is excluded

Given the equation

4x + 3 = 23

4x = 23 - 3

4x =20

x = 5

Hence 5 is the solution from the given set

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A seesaw has a plank of 4.5 m long which is supported by a pivot at its center and moves in a vertical plane above the pivot. If the height of the pivot pillar above the ground is 1 m, through what maximum angle can the seesaw beam move?

Answers

Since the pivot pillar is 1 m above the ground, maximum angle can the seesaw beam move is 26.39°

The maximum angle can be gotten using trigonometric ratios answer the question,

What are trigonometric ratios?

Trigonometric ratios are the ratios of the sides of a triangle.

What are angles?

Angles are a measure of rotation or bearing.

Given that the seesaw plank is 4.5 m long and the pivot pillar is 1 m above the ground, when the seesaw is at maximum angle, it forms a right angled triangle with the ground.

It also forms a smaller similar triangle with the same maximum angle Ф which is gotten from the trigonometric ratio

sinФ = h/L where

h = height of pivot pillar above ground = 1 m and L = length of midpoint of plank = 4.5m/2 = 2.25 mMaximum angle seesaw beam can move

So, Ф = sin⁻¹(h/L)

= sin⁻¹(1 m/2.25 m)

= sin⁻¹(1/2.25)

= sin⁻¹(0.4444)

= 26.39°

So, maximum angle can the seesaw beam move is 26.39°

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Mrs. Eaton's dass is participating in the "Box Teps for Education campaign. On the first day, her
class collected 2 lops. On the third day, her dass collected 8 tope. Let D represent each collection
day and N represent the number of tops collected on that day.
Based on the situation, John daims the number of tops colected can be modeled by an exponential
function. Riley disagrees and claims the number of tops can be modeled with a linear function. What
Is the number of tops collected on the abath day based on the exponential model? What is the
number of tops collected on the sixth day based on the linear model?
Number of tops on 6th day based on exponential model:
Number of tops on the 6th day based on the linear model:

Answers

The number of tops on the 6th day based on the exponential model is 64, and the number of tops on the 6th day based on the linear model is 17.

What is an exponential function?

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent [tex]\rm y = a^x[/tex]

where a is a constant and a>1

First day class collected = 2 tops

Third day class collected = 8 tops

The exponential function can be modelled:

[tex]\rm D(N) = 2^N[/tex]

D(1) = 2  (first day)

D(3) = 8  (third day)

D(6) = 64 (sixth day)

The linear function can be modeled:

D(N) = 3N -1

D(1) = 2  (first day)

D(3) = 8 (third day)

D(6) = 17 (sixth day)

Thus, the number of tops on 6th day based on exponential model is 64, and the number of tops on the 6th day based on the linear model is 17.

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how many times greater is the vuale in 4 in 547 than 4 in 84

Answers

Answer:

10 times

Step-by-step explanation:

4 in 547 is equal to 40

4 in 84 is equal to 4

When you separate that number into smaller parts

Ex: 547 = 500 + 40 + 7

find x if the ekvation is
x-3x+7x/2-1=9

Answers

Step-by-step explanation:

i got confused whether it is 7/2 or /2-1

I need help for brainliest

Answers

Answer:

46 cm²

Step-by-step explanation

the figure is composed of a square with an isosceles right triangle inside, we find the area of ​​the square and we take away the area of ​​the triangle.

Triangle area = lxl, right-angled triangle area side by side divided by two.

square area

8 * 8 = 64cm²

Triangle area

6 * 6 : 2 = 18 cm²

Area of the shaded region

64 - 18 = 46 cm²

theres 1 circle split into 4 parts 1/4 in each and another circle with 8 parts and 1/8 in each m/4=6/8

Answers

Answer:

m = 3

Step-by-step explanation:

see image.

6/8 = 3/4

Use the picture in the problem or use algebra to find m. See image.

Which could be a first step in solving the equation
1/4 x + 1/2 = 3/4x
in an efficient way? Select two answers.

A.
multiply by 4 on both sides

B.
multiply by 2x on both sides

C.
subtract 1/4x from both sides

D.
add 1/2 from both sides

Answers

A first step in solving the equation 1/4 x + 1/2 = 3/4x will be answer A multipllied by 4 on both sides.

What is an equation?

The equation is actually a relationship between the numbers and the variables.The given equation is  1/4 x + 1/2 = 3/4x

Now the solution of the equation will be:-

1/4 x + 1/2 = 3/4x

By multiplying with 4 the equation will become:-

x+2=3x

3x-x=2

2x=2

x=1

Hence the solution of the given equation will be x=1

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Answer:A

Step-by-step explanation:

Multiplying each by 1/4.We have;4x1/4 + 4x1/2 = 4x3/44/4 + 4/2 = 12/41 + 2 = 33=3This is the most effective way.

Find the area inside one leaf of the rose: r=6sin(6theta)

Answers

The area inside one leaf of the rose: r=6sin(6θ) is 3π/2 after evaluating the integral over the limit 0 to  π/6

What is integration?

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

We have:

r=6sin(6θ)

First we have to find the limits:

r = 0

6sin(6θ) = 0

θ = nπ/6

n = 0 to n = 1

θ = 0 to  θ = π/6

[tex]\rm Area = \int\limits^{\dfrac{\pi}{6}}_0 {6sin6\theta} \, d\theta[/tex]

After calculating the above definite integral, we will get:

Area = 3π/2

Thus, the area inside one leaf of the rose: r=6sin(6θ) is 3π/2 after evaluating the integral over the limit 0 to  π/6

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evaluate the expression [tex](-0.3)^4[/tex]
the value of the expression is

Answers

The value of the expressions (-0.3)⁴ equal to 0.0081.

What is a mathematical expression?

A mathematical expression is the representation of numbers in the form of powers or mathematical signs.

Here we have the (-0.3)⁴

Now by evaluating the expression we will get:

(-0.3)⁴=(-0.3x-0.3x-0.3x-0.3)

Hence the value of the given expression will be 0.0081

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Cole ate 2/3 of the cookies in the cookie jar. Jim ate 1/4 of the cookies
left. If the cookie jar started with two-dozen cookies, how many cookies
are still in the jar?

Answers

Answer:

6

Step-by-step explanation:

first, we start with 2 dozen = 2 * 12 = 24 cookies

next, cole eats 2/3 of the cookies

2/3 of the cookies = 2/3 * 24 = 16

we are then left with

original # - # of cookies cole ate = 24 - 16 = 8

next, jim eats 1/4 of the cookies left

cookies left = 8

1/4 of cookies left = 1/4 * 8 = 2

cookies left - cookies jim eats = cookies still in jar = 8 - 2 = 6

Other Questions
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