Donna is making a cookie recipe that calls for 1 ¾ cups of sugar. However, when she

goes to take out the measuring cups she can only find the one-half cup measuring cup. How many one-half cups will she need to fill to get the correct amount of sugar for her cookie recipe?

Using an exponential function, it is found that the multiplier that would allow you to predict the population of bacteria after 2 hours is of 9.

An exponential function is modeled by:

[tex]y = ab^x[/tex]

In which:

In this problem, the bacteria triples every hour, hence the rate of change is b = 3, and the equation is:

[tex]y = a(3)^x[/tex]

Hence, after 2 hours:

[tex]y = a(3)^2 = 9a[/tex]

Which means that the multiplier is of 9.

More can be learned about exponential functions at https://brainly.com/question/25537936

#SPJ1

The value of y in the given logarithmic equation is 3. The correct option is C. 3

From the question, we are to determine the value of y in the given logarithmic equation

The given equation is

[tex]log_{4}64=y[/tex]

By applying one of the laws of logarithm, we get

[tex]64 = 4^{y}[/tex]

Now, express 64 in index form,

[tex]4^{3} = 4^{y}[/tex]

Since the bases are equal, we can equal the powers to get

3 = y

∴ y = 3

Hence, the value of y in the given logarithmic equation is 3. The correct option is C. 3

Learn more on Logarithmic equations here: https://brainly.com/question/237323

#SPJ1

Answer:

Computer game designer.

Step-by-step explanation:

If you want to design a game, you need to have some basic shapes and stuff in it. I'm not sure what else needs to be explained here lol

Answer:

-2.6

Step-by-step explanation:

-1.4+(-1.2)

-1.4-1.2=-2.6

Hope this helps!

If not, I am sorry.

Answer:

A=2, B=3, C=5

Step-by-step explanation:

Two polynomials are equal for all values of the variable if the corresponding coefficients are the same. The way to solve the problem is to multiply the RHS, rewrite it in a more orderly way

[tex](Ax-1)(x-B)(x+1)+C = \\Ax^3+(A-AB-1)x^2+(B-AB-1)x +B+C[/tex]

Now, for the two polynomials to be the same we need to have, at the same time

[tex]x^3: A=2\\x^2: A-AB-1= -5\\x:B-AB-1=-4\\1: B+C=8[/tex]

You might notice that we have more conditions than variables, but you can consider one of the two in the middle as a "check" option.

Now, grabbing the value from the first condition into the second we get B=3. Replacing both value in the third we see that the equality still holds, and replacing into the fourth we get C =5.

Answer:

give clear image is next question

Step-by-step explanation:

i will give you the answer

Answer:

Range = 1 1/4

Step-by-step explanation:

Range = Maximum - Minimum

Arranging the data in ascending order :

Solving for range :

The amount of plywood that he needs to buy will be 21 square feet.

Let the prism with a length of L of the rectangular surface.

And the dimension of the triangle is A, B, and C. Then we have

SA = 2(area of triangle) + 3(area of rectangle surface)

A triangular prism.

The rectangular sides are 3 feet by 2 feet, 3 feet by 2.5 feet, and 3 feet by 1.5 feet.

The 2 triangular sides have a base of 2 feet and a height of 1.5 feet.

Then the area of the triangle will be

⇒ 1/2 x 2 x 1.5

⇒ 1.5 square feet

The area of the rectangles will be

⇒ 3 x 2 + 3 x 2.5 + 3 x 1.5

⇒ 18 square feet

Then the surface area of the triangular prism will be

Surface area = 2 x 1.5 + 18

Surface arae = 3 + 18

Surface area = 21 square feet

More about the surface area of the triangular prism link is given below.

https://brainly.com/question/16765719

#SPJ1

A group of students from your school is part of the audience for a TV game show, the theoretical probability of students is mathematically given as  

P=2.7%

Generally, the equation for Probability  is mathematically given as

[tex]P=\frac{Desired outcomes}{Total outcomes}[/tex]

Where Desired outcomes

D=40C5 *110C3

D=1420112865560

And Total outcomes

T=150C8 *

T=5.2572*10^10{12}

Hence, Probability  

[tex]P=1420112865560/ 5.2572*10^10{12}[/tex]

P=0.0270

P=2.7%

In conclusion, the theoretical probability

P=2.7%

Read more about probability

https://brainly.com/question/11234923

#SPJ1

[tex]\huge\sf\underline{Answer}[/tex]

Let's find out ~

Given :-

Solution :-

[tex]\sf\rightarrow \:LSA \: of \: cuboid \: = 2h \: ( \: l + b \: )[/tex]

[tex]\sf\rightarrow \: 180 = 2h \: (10 + 5)[/tex]

[tex]\sf\rightarrow180 = 2h \: \times 15[/tex]

[tex]\sf\rightarrow 180 = 30h \: [/tex]

[tex]\sf\rightarrow \: 30h \: = 180[/tex]

[tex]\sf\rightarrow \: h = \frac{180}{30} [/tex]

[tex]\sf\rightarrow \: 6[/tex]

Thus , the height of cuboid is 6m

Answer:

Step-by-step explanation:

We can classify triangles by their sides into three types:

Explanation:

The value of 'a' out front in y = a sin(bx) determines the amplitude.

The b term helps us compute the period, which is 2pi/b for sine, cosine, secant, and cosecant functions.

For example, y = 2sin(3x) has an amplitude of 2 and period of 2pi/3

For tangent and cotangent functions, the period would be pi/b.

Part 1

V = pi*r^2*h .... volume of a cylinder

250 = pi*r^2*h

h = 250/(pi*r^2)

Plug this into the surface area of a cylinder equation

SA = 2*pi*r^2 + 2*pi*r*h

SA = 2*pi*r^2 + 2*pi*r*( 250/(pi*r^2) )

SA = 2*pi*r^2 + 500/r

Now replace every copy of r with x to get this function

f(x) = 2*pi*x^2 + 500/x

x = radius

y = f(x) = surface area

Next we'll use Desmos to graph this function. See the screenshot below. It produces some kind of curve that has two pieces to it. We'll only focus on the curve where x > 0 and y > 0. It makes no sense to have a negative radius, and we cannot have a negative surface area either.

Click on the lowest point of the parabolic looking shaped piece (it's not really a parabola, but we'll imagine that it is for the sake of simplicity).

The coordinates of that local min point will show up and they are (3.414, 219.689)

We have (x,y) = (3.414, 219.689) lead to r = 3.414 and SA = 219.689

This means that a radius of approximately r = 3.414 cm leads to the smallest surface area of approximately 219.689 square cm. This is when the amount of material is minimized.

Use this value of r to find h

h = 250/(pi*r^2)

h = 250/(pi*3.414^2)

h = 6.828

Desmos not only graphs, but it is also a standard calculator. The calculation is also shown in the screenshot.

=============================================================

Part 2

Point L is the midpoint

The midpoint is halfway between the two points. In this case, Point F and Point B are 10 units away from each other. The midpoint is the distance between the points (10) divided by 2.

Answer:

250.000$

Step-by-step explanation:

so you multiple 2.000 by 25

The statement that can never be true is the data set contains a value of 3.

A box plot is used to study the distribution of a dataset. The box plot consists of two lines and a box. The two lines are known as whiskers. The end of the first line represents the minimum number and the end of the second line represents the maximum number.

minimum number = 8

maximum number = 22

To learn more about box plots, please check: brainly.com/question/27215146

#SPJ1

Answer:

(2,-4)

Step-by-step explanation:

Here, h=2 and k=-4, so the center is (2,-4)

Answer: 432

Step-by-step explanation:

  12

x 36

--------

    72

+ 36

-------

432

Using the z-distribution, it is found that the margin of error for the 95% confidence interval is of 0.0889.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The estimate and the sample size are given as follows:

[tex]\pi = 0.71, n = 100[/tex]

Hence, the margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]M = 1.96\sqrt{\frac{0.71(0.29)}{100}}[/tex]

M = 0.0889.

More can be learned about the z-distribution at https://brainly.com/question/25890103

#SPJ1

Answer:

reason 1.) This is the original expression

reason 2.) you subtract 4 from both sides

reason 3.) you divide both sides by 2 to get x=5

Answer:

38.1971

Step-by-step explanation:

The formula for diameter is circumference/ pi. So 120/3.14... is 38.1971

Answer:

the value of b to 2

The value of b changes to 2.

The correct option is C.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.

We have,

Equation: h(x) = -x + 5

Now, using the slope intercept form

y = mx + b

From which we get

m = -1 and b=5

Now, we need to move the graph 3 units down then we need to subtract given function by 3, we get

y = -x+5 -3

y = -x +2.

Here y-intercept is 2.

Learn more about Linear Equation here:

https://brainly.com/question/4025726

#SPJ7

[tex]\text{L.H.S}\\\\=\cot^2 \dfrac{\pi}6 -2\cos^2 \dfrac{\pi}{3}-\dfrac 34 \sec^2 \dfrac{\pi}4-4\sec^2 \dfrac{\pi}6\\\\\\=\cot^2 30^\circ -2 \cos^2 60^\circ- \dfrac 34 \sec^2 45^{\circ} -4 \sec^2 30^{\circ}~~~~~~~;[\pi= 180^{\circ}]\\\\\\=\left(\sqrt 3 \right)^2 -2 \left( \dfrac 12 \right)^2 -\dfrac 34 \left(\sqrt 2 \right)^2 -4 \left(\dfrac 2{\sqrt 3} \right)^2\\\\\\=3-2 \cdot \dfrac 14 - \dfrac 34 \cdot 2 -4 \cdot \dfrac 43\\ \\\\=3-\dfrac 12-\dfrac 32 - \dfrac{16}3\\\\\\[/tex]

[tex]\\=\dfrac{9-16} 3 - \dfrac 42 \\\\\\=\dfrac{-7}{3}-2\\\\\\=\dfrac{-7-6}3\\\\\\=-\dfrac{13}3\\\\\\=-4\dfrac 13 \\\\\\=\text{R.H.S}\\\\\\\text{Proved.}[/tex]

Answer:

Points on the inverse are [tex](1,-1), (4,2), \text{and } (0,0)[/tex]

Step-by-step explanation:

When writing the inverse function of a set of points, you simply switch the coordinates:

[tex]\text{Function}: (x,y)\\\text{Inverse}: (y,x)[/tex]

We are given the points

[tex](-3,9), (-1,1), (0,0), \text{and } (2,4)[/tex]

Using our rule for function, our new points will be

[tex](9,-3), (1,-1), (0,0), \text{and } (4,2)[/tex]

From the list, the points we have for the graph of the inverse are

[tex](1,-1), (4,2), \text{and } (0,0).[/tex]

Answer:

x = z - m + y

Step-by-step explanation:

Given:

[tex]\displaystyle \large{z = m+x-y}[/tex]

To solve for x-term, we have to isolate it. We can do by subtracting m-term both sides and add y-term both sides.

[tex]\displaystyle \large{z-m+y=m+x-y-m+y}\\\\\displaystyle \large{z-m+y=x}\\\\\displaystyle \large{x=z-m+y}[/tex]

Therefore, the answer to this question is x = z - m + y

Please let me know if you have any questions regarding my answer or explanation!

to get the equation of any straight line, we simply need two points off of it, so let's use the ones provided in the table above.

[tex]\begin{array}{|cc|ll} \cline{1-2} \stackrel{millions}{population}&year\\ \cline{1-2} 161&1950\\ 291&2000\\ \cline{1-2} \end{array}\hspace{5em} (\stackrel{x_1}{161}~,~\stackrel{y_1}{1950})\qquad (\stackrel{x_2}{291}~,~\stackrel{y_2}{2000}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2000}-\stackrel{y1}{1950}}}{\underset{run} {\underset{x_2}{291}-\underset{x_1}{161}}} \implies \cfrac{ 50 }{ 130 }\implies \cfrac{5}{13}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1950}=\stackrel{m}{\cfrac{5}{13}}(x-\stackrel{x_1}{161}) \\\\\\ y-1950=\cfrac{5}{13}x-\cfrac{805}{13}\implies y=\cfrac{5}{13}x-\cfrac{805}{13}+1950\implies y=\cfrac{5}{13}x+\cfrac{24545}{13}[/tex]

Answer:

6√x

Step-by-step explanation:

9√x - 3√x = 6√x

Answer:

She is wrong.

Step-by-step explanation:

The mean score is

7 + 8 + 3 + 0 + 2= 20

We then divide it by the number which is 5

20/5= 4.

Therefore, Maria is wrong.

This is because she divided by 4 instead of 5, as she didn't include the rational number 0.

Answer:

b. x = 123

Step-by-step explanation:

Answer:

Hi,

Step-by-step explanation:

Answer B : 51

1+4+7+10+13+16=51