The manager at a smoothie stand keeps track of the number of protein smoothies and berry smoothies sold each day and the total money received. On Saturday, a total of 43 smoothies were sold, and the money collected was $314. If protein smoothies are sold for $10 and berry smoothies are sold for $6, how many protein smoothies and berry smoothies were sold?

Answer:

√65

Step-by-step explanation:

you have to use the pythagoras theorem to find x which is the hypotenuse

x²=7²+4²

x²=49+16

√x²=√65

x=√65

I hope this helps

Answer:

9

Step-by-step explanation:

90+81+mising angle=180, missing angle is 9

Answer:

(-5, 0) and (5, 0)

Step-by-step explanation:

This equation fits the form for a hyperbola with x-intercepts.  The standard form for such an equation is

[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]

To get the equation in the question into this standard form, divide each term by 400.

[tex]\frac{16x^2}{400}-\frac{25y^2}{400}=\frac{400}{400}\\\frac{x^2}{25}-\frac{y^2}{16}=1[/tex]

To find the x-intercepts, make y = 0.

[tex]\frac{x^2}{25}=1\\x^2=25\\x=\pm 5[/tex]

The vertices are located at the points (-5, 0) and (5, 0).

Note: There are no y-intercepts; making x = 0 produces no real solutions for y.

Answer:

y = -1x + 2

Step-by-step explanation:

9514 1404 393

Answer:

  x = √2

Step-by-step explanation:

A graph indicates the only solution is near x=√2.

__

Square both sides, separate the radical and do it again.

  [tex]\displaystyle(2-x)\sqrt{\frac{x+2}{x-1}}=\sqrt{x}+\sqrt{3x-4}\qquad\text{given}\\\\(2-x)^2\cdot\frac{x+2}{x-1}=x+(3x-4)+2\sqrt{x(3x-4)}\qquad\text{square}\\\\\frac{(2-x)^2(x+2)}{x-1}-4x+4=2\sqrt{x(3x-4)}\qquad\text{isolate radical}\\\\\left(\frac{(2-x)^2(x+2)-4(x-1)^2}{x-1}\right)^2=x(3x-4)\qquad\text{square}\\\\(x^3-6x^2+4x+4)^2=4(x-1)^2(3x^2-4x)\qquad\text{multiply by $(x-1)^2$}[/tex]

Now, we can put this polynomial equation into standard form and factor it.

  [tex]x^6 -12x^5+32x^4-76x^2+48x+16=0\\\\(x-2)^2(x^2-2)(x^2-8x-2)=0\qquad\text{factor it}\\\\x\in \{2,\pm\sqrt{2},4\pm3\sqrt{2}\}[/tex]

The original equation requires that we restrict the domain of possible solutions. In order for the radicals to be non-negative, we must have x ≥ 4/3. In order for the left side of the equation to be non-negative, we must have x ≤ 2. So, the only potential solutions will be in the interval [4/3, 2].

The only values in the above list that match this requirement are {√2, 2}. We know that the right side of the equation cannot be zero, so the value x=2 is also an extraneous solution.

The only solution is x = √2.

_____

Additional comment

For solving higher-degree polynomials, I like to use a graphing calculator to help me find the roots. The second attachment shows the roots of the 6th-degree polynomial. They can help us factor the equation. (There are also various machine solvers available that will show factors and roots.)

Answer:

The correct answer is - C. 24.1%

Step-by-step explanation:

Given:

mean μ = 65%

standard deviation δ = 7.1 %

solution:

Prob( X>70) = 1 - Prob(x<70)  

= P (x-μ/δ ≥ 70 -65/7.1)

= 1 - Prob( (70-65)/7.1)

= 1 - Prob ( z < 0.7042553)

= 0.24065

the percentage of students scoring 70 or more in the exam

= 24.065*100

= 24.1%

Answer:

g(x)

because it is a quadratic equation it is mirrored the other one isn’t even a function

The true statement is The functions f and g have the same axis of symmetry, and the maximum value of f is greater than the maximum value of g.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

The function g has the axis of symmetry as x = 2, since the values of the function below and above x = 2 changes in the same way.

The function f is a parabola.

The axis of symmetry is also x = 2, since the graph is the same before and after the line x = 2.

So the both the functions have same axis of symmetry.

Maximum value of the function f = 4 at x = 2. Since no other values of f is greater than 4.

At x = 2, the value of g = 3

Maximum value of g = 3

So, maximum value of f is greater than the maximum value of g.

Hence the correct option is B.

Learn more about Functions here :

https://brainly.com/question/14708365

#SPJ7

Your question is incomplete. The complete question is as given below.

The graph shows the quadratic function f and the table shows the quadratic function g.

x   : -2     -1      0      1      2      3      4

g(x) -1   0.75    2   2.75   3    2.75   2

Which statement is true?

The functions f and g have the same axis of symmetry, and the maximum value of f is less than the maximum value of g.

The functions f and g have the same axis of symmetry, and the maximum value of f is greater than the maximum value of g.

The functions f and g have different axes of symmetry and different maximum values.

The functions f and g have the same axis of symmetry and the same maximum values.

BBBBB BBBBBBBBBBBBBBBBBBBBBBBBBBBB

Answer:

26 + 3 x 42 + 7 x -2 = 138

Step-by-step explanation:

Ok bud, first step we must convert our symbols (Makes it easier to solve)

26 + 3 x 42 + 7 x -2

* subsitutes for multiplication.

I recommend using PEMDAS at times:

1 - Parentheses

2 - Exponents and Roots

3 - Multiplication

4 - Division

5 - Addition

6 - Subtraction

Yet again your numbers were spaced out could they be exponents? if so:

3x^{42}+7x+24

Our answer would round to 24 but he equation was not put in a valid or straight forward way.

Using the shell method, the volume integral would be

[tex]\displaystyle 2\pi \int_0^2 x(256-x^8)\,\mathrm dx[/tex]

That is, each shell has a radius of x (the distance from a given x in the interval [0, 2] to the axis of revolution, x = 0) and a height equal to the difference between the boundary curves y = x ⁸ and y = 256. Each shell contributes an infinitesimal volume of 2π (radius) (height) (thickness), so the total volume of the overall solid would be obtained by integrating over [0, 2].

The volume itself would be

[tex]\displaystyle 2\pi \int_0^2 x(256-x^8)\,\mathrm dx = 2\pi \left(128x^2-\frac1{10}x^{10}\right)\bigg|_{x=0}^{x=2} = \boxed{\frac{4096\pi}5}[/tex]

Using the disk method, the integral for volume would be

[tex]\displaystyle \pi \int_0^{256} \left(\sqrt[8]{y}\right)^2\,\mathrm dy = \pi \int_0^{256} \sqrt[4]{y}\,\mathrm dy[/tex]

where each disk would have a radius of x = ⁸√y (which comes from solving y = x ⁸ for x) and an infinitesimal height, such that each disk contributes an infinitesimal volume of π (radius)² (height). You would end up with the same volume, 4096π/5.

The volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis is 4096π/5 cubic units.

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

We have a function:

[tex]\rm y = x^8[/tex]   or

[tex]x = \sqrt[8]{y}[/tex]

And  y = 256

By using the vertical axis of rotation method to evaluate the volume of the solid formed by revolving the region bounded by the curves.

[tex]\rm V = \pi \int\limits^a_b {x^2} \, dy[/tex]

Here a = 256, b = 0, and [tex]x = \sqrt[8]{y}[/tex]

[tex]\rm V = \pi \int\limits^{256}_0 {(\sqrt[8]{y}^2) } \, dy[/tex]

After solving definite integration, we will get:

[tex]\rm V = \pi(\frac{4096}{5} )[/tex]  or

[tex]\rm V =\frac{4096}{5}\pi[/tex] cubic unit

Thus, the volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis is 4096π/5 cubic units.

Learn more about integration here:

brainly.com/question/18125359

Answer:

The proportion of bottles that will have more than 30 ounces dispensed into them is 0.9772 = 97.72%.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The amount dispensed has been observed to be approximately normally distributed with mean 32 ounces and standard deviation 1 ounce.

This means that [tex]\mu = 32, \sigma = 1[/tex]

Determine the proportion of bottles that will have more than 30 ounces dispensed into them.

This is 1 subtracted by the p-value of Z when X = 30, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{30 - 32}{1}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a p-value of 0.0228.

1 - 0.0228 = 0.9772

The proportion of bottles that will have more than 30 ounces dispensed into them is 0.9772 = 97.72%.

Answer:

A. 50º

Step-by-step explanation:

we are given the exterior angles 140º and 90º

exterior angles + corresponding interior angles = 180º

that means the two other angles of the triangle are:

180 - 140 = 40º

and

180 - 90 = 90º

the sum of interior angles in a triangle = 180

p = 180 - (40 + 90)

p = 180 - 130

p = 50º

Answer:

the first option because I took the test

Answer:

✔ positive

✔ 1

✔ closely

✔ increases

ED2021

Answer:

(2,0)

Step-by-step explanation:

the x intercept is when 'y' is equal to 0 :

0 = 3x - 6

6 = 3x

x = 2

Answer:

(2,0)

Step-by-step explanation:

y = 3x-6

The x intercept is found by setting y = 0 and solving for x

0 = 3x-6

Add 6 to each side

6 = 3x-6+6

6 =3x

Divide each side by 3

6/3 = 3x/3

2 =x

The x intercept is

(2,0)

By observing the points you can learn a lot about a function. Concretely [tex]f(x)[/tex] passes through [tex](1,1)[/tex] but [tex]g(x)[/tex] passes through [tex](1,-\frac{1}{2})[/tex] that should give you a hint that [tex]g(x)=-\frac{1}{2}x^2[/tex].

Hope this helps :)

Answer:

(c) (f-g ) (x) = 6x*3 -2x*2 +4x -8

Answer:

Hi! I'll provide the answers in the explanation.

Step-by-step explanation:

a) The table is in the attachment.

b) The percentage is 40%. Looking at the table, we can see that the total of teachers who voted is 30. You'll be able to find the percentage if you divide 30/75, since 75 is the total people who took the survey.

c) The percentage is 40%. For this situation, we have to divide the total of the people who voted for NO by the teachers who voted NO. So it'll be 20/50, which is 0.4. We can simplify that and the solution is 40%.

d) It represents the students who took the survey voted NO for a later start.

Hope this helps! :D

Answer:

5. Use the following information to answer the questions.

A survey asked 75 people if they wanted a later school day start time.

45 people were students, and the rest were teachers.

50 people voted yes for the later start.

30 students voted yes for the later start.

a) Use this information to complete the frequency table. (5 points: 1 point for each cell that was not given above)

Vote YES for later start

Vote NO for later start

Total

Students

30

15

45

Teachers

20

10

30

Total

50

25

75

b) Use the completed table from Part a. What percentage of the people surveyed were teachers? (2 points)

40%

c) Use the completed table from Part a. What percentage of the people surveyed were teachers who wanted a later start time? (2 points)

40%

d) What does the number in the bolded cell represent? (1 point)

The number of students that said no to a later start.

Step-by-step explanation:

A p E x

Answer:

they sold 64hotdogs and 128 sodas

Step-by-step explanation:

2x+x=192 3x=192 x=64

The area of the larger circle is 81π square units.

Congruent circles are circles that are similar in pattern.

The formula for calculating the area of a circle is expressed as:

[tex]A = \dfrac{\pi d^2}{4}[/tex]

Given that the area of each of the small circles is 9π, then:

[tex]9 \pi =\frac{\pi d^2}{4}\\9 = \frac{d^2}{4}\\d^2=9*4\\d^2=36\\d=\sqrt{36}\\d=6units[/tex]

This shows that the diameter of one of the small circles is 6units.

Since the diameter of the three circles will be equivalent to the diameter of the larger circle, hence;

Diameter of the larger circle = 3(6) = 18units

Get the area of the larger circle:

[tex]A=\frac{\pi D^2}{4}\\A=\frac{\pi \times 18^2}{4}\\A =\frac{324\pi}{4}\\A= 81\pi[/tex]

Hence the area of the larger circle is 81π square units.

Learn more on the area of circles here: https://brainly.com/question/12298717

Answer:

The null hypothesis is [tex]H_0: \sigma = 0.3[/tex]

The alternative hypothesis is [tex]H_1: \sigma \neq 0.3[/tex]

Step-by-step explanation:

Test if the tar content of filtered​ 100-mm cigarettes has a standard deviation different from 0.30 ​mg.

At the null hypothesis, we test if the standard deviation is of 0.3, that is:

[tex]H_0: \sigma = 0.3[/tex]

At the alternative hypothesis, we test if the standard deviation is different of 0.3, that is:

[tex]H_1: \sigma \neq 0.3[/tex]

Answer:

C.    AA

Step-by-step explanation:

Since m<Y = 27°, then m<W = 27°.

We have two angles of one triangle (A and B) congruent to two angles of the other triangle (W and X).

Answer: C.   AA

Answer: 6669

Step-by-step explanation:

I hope I did this right... anyways,

t, is represented by years, which is given to us by 2 years and 9 months. Assuming you would put 2.9 for t.

Additionally, as you can't have a decimal for a person, and they've asked for it to be rounded to the nearest whole number, there would be 6669 people in 2 years and 9 months.

The formula used is:

[tex]7285(0.97)^2^.^9[/tex]

Answer:

Individual is represented by a single point

Step-by-step explanation:

Answer:

x = 38.4

Step-by-step explanation:

tan(38) = 30/x

x = 30/tan(38)

x = 38.4

Answered by GAUTHMATH

Answer:

[tex]g(-1) = -1[/tex]

[tex]g(0.75) = 0[/tex]

[tex]g(1)= 1[/tex]

Step-by-step explanation:

Given

See attachment

Solving (a): g(-1)

We make use of:

[tex]g(x) = -1[/tex]

Because: [tex]-1 \le x < 0[/tex] is true for x =-1

Hence:

[tex]g(-1) = -1[/tex]

Solving (b): g(0.75)

We make use of:

[tex]g(x) = 0[/tex]

Because: [tex]0 \le x < 1[/tex] is true for x =0.75

Hence:

[tex]g(0.75) = 0[/tex]

Solving (b): g(1)

We make use of:

[tex]g(x) = 1[/tex]

Because: [tex]1 \le x < 2[/tex] is true for x =1

Hence:

[tex]g(1)= 1[/tex]

Answer:

28  and 38

Step-by-step explanation:

a+b = 66

a + 10 = b

using substitution, a + (a+10) = 66

2a = 56

a = 28

28 + 10 = 38

b = 38

Answer:

B

Step-by-step explanation:

(-2/3x)-10<1/3

(-2/3x)<1/3+10

(-2/3x)<31/3

x>-31/2, -31/2=-15 (1/2), x> - 15 (1/2)

Answer:

pentagons

Step-by-step explanation:

In fact, there are pentagons which do not tessellate the plane. The house pentagon has two right angles. Because those two angles sum to 180° they can fit along a line, and the other three angles sum to 360° (= 540° - 180°) and fit around a vertex.

Answer:

The Regular Pentagon.

Explanation

I got a 100 % on the quiz