Lisa purchased groceries worth $34 for a party. A gallon of milk costs $2.50, a gallon of ice cream costs $7.50, and a gallon of lemonade costs $3.00
If Lisa bought 4 gallons of milk, and 2 gallons of ice cream, how many gallons of lemonade did she buy?
Answer 1: 5
Answer 2: 3
Answer 3: 2
Answer 4: 4

To test whether there is evidence to support the claim that catalyst 2 produces a higher mean yield than catalyst 1, a two-sample t-test can be performed. To find a 99% confidence interval on the difference in mean yields, a formula can be used.

To test whether there is evidence to support the claim that catalyst 2 produces a higher mean yield than catalyst 1, we can perform a two-sample t-test.

(b) To find a 99% confidence interval on the difference in mean yields, we can use the formula: CI = (mean1 - mean2) ± (critical t-value * standard error), where standard error = sqrt((standard deviation1^2/n1) + (standard deviation2^2/n2)).

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(a) Yes, there is evidence to support the claim that catalyst 2 produces a higher mean yield than catalyst 1.

(b) The 99% confidence interval on the difference in mean yields is approximately (-6.52, -1.48).

(a) To test whether there is evidence to support the claim that catalyst 2 produces a higher mean yield than catalyst 1, we can conduct a hypothesis test.

- Null Hypothesis [tex](\(H_0\))[/tex]:

The mean yield produced by catalyst 2 is not higher than the mean yield produced by catalyst 1. [tex]\( \mu_1 \geq \mu_2 \)[/tex]

- Alternative Hypothesis [tex](\(H_1\))[/tex]:

The mean yield produced by catalyst 2 is higher than the mean yield produced by catalyst 1. [tex]\( \mu_1 < \mu_2 \)[/tex]

We'll use a two-sample t-test for independent samples since we are comparing the means of two independent groups.

Given:

- Sample mean [tex](\( \bar{x}_1 \))[/tex] for catalyst 1 = 85

- Sample mean [tex](\( \bar{x}_2 \))[/tex] for catalyst 2 = 89

- Sample standard deviation [tex](\( s_1 \))[/tex] for catalyst 1 = 3

- Sample standard deviation ([tex]\( s_2 \)[/tex]) for catalyst 2 = 2

- Sample size [tex](\( n_1 \))[/tex] for catalyst 1 = 12

- Sample size [tex](\( n_2 \))[/tex] for catalyst 2 = 15

- Degrees of freedom [tex](\( df \)) = \( n_1 + n_2 - 2 \)[/tex]

Let's calculate the t-statistic:

[tex]\[ t = \frac{(\bar{x}_1 - \bar{x}_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} \][/tex]

[tex]\[ t = \frac{(85 - 89)}{\sqrt{\frac{3^2}{12} + \frac{2^2}{15}}} \][/tex]

[tex]\[ t \approx \frac{-4}{\sqrt{\frac{9}{12} + \frac{4}{15}}} \][/tex]

[tex]\[ t \approx \frac{-4}{\sqrt{0.75 + 0.2667}} \][/tex]

[tex]\[ t \approx \frac{-4}{\sqrt{1.0167}} \][/tex]

[tex]\[ t \approx \frac{-4}{1.0083} \][/tex]

[tex]\[ t \approx -3.97 \][/tex]

Now, we'll find the critical value for the t-distribution with the given degrees of freedom and a one-tailed test at a 99% confidence level.

Since it's a one-tailed test, we're interested in the critical value to the right of the distribution.

Using a t-table or a statistical software, the critical value for a one-tailed test with [tex]\( df = 12 + 15 - 2 = 25 \)[/tex] and [tex]\( \alpha = 0.01 \)[/tex] is approximately [tex]\( t_{\text{critical}} \approx 2.492 \)[/tex].

Since [tex]\( t = -3.97 < t_{\text{critical}} = 2.492 \)[/tex]we reject the null hypothesis.

Therefore, there is evidence to support the claim that catalyst 2 produces a higher mean yield than catalyst 1.

(b) To find a 99% confidence interval on the difference in mean yields, we'll use the formula:

[tex]\[ \text{Confidence Interval} = (\bar{x}_1 - \bar{x}_2) \pm t_{\alpha/2} \times \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} \][/tex]

Substituting the given values:

[tex]\[ \text{Confidence Interval} = (85 - 89) \pm 2.492 \times \sqrt{\frac{3^2}{12} + \frac{2^2}{15}} \][/tex]

[tex]\[ \text{Confidence Interval} = -4 \pm 2.492 \times \sqrt{0.75 + 0.2667} \][/tex]

[tex]\[ \text{Confidence Interval} = -4 \pm 2.492 \times \sqrt{1.0167} \][/tex]

[tex]\[ \text{Confidence Interval} = -4 \pm 2.492 \times 1.0083 \][/tex]

[tex]\[ \text{Confidence Interval} = -4 \pm 2.5161 \][/tex]

[tex]\[ \text{Confidence Interval} = (-6.5161, -1.4839) \][/tex]

Rounded to two decimal places, the 99% confidence interval on the difference in mean yields is approximately (-6.52, -1.48).

Answer:

Part A) [tex]500\ ft[/tex]

Part B) [tex]2\ in[/tex]

Step-by-step explanation:

we know that

The scale of the map is [tex]\frac{1}{125} \frac{in}{ft}[/tex]

That means

1 in on the map represent 125 ft in the real

Part A) How many feet do 4 inches

using proportion

[tex]\frac{1}{125} \frac{in}{ft}=\frac{4}{x} \frac{in}{ft}\\ \\x=125*4\\ \\x=500\ ft[/tex]

Part B) Jon lives 250 feet away from Max. How many inches separate Jon’s home from Max’s on the map?

using proportion

[tex]\frac{1}{125} \frac{in}{ft}=\frac{x}{250} \frac{in}{ft}\\ \\x=250/125\\ \\x=2\ in[/tex]

Jon's home is 2 inches from Max's on the map, according to the scale of 1 inch:125 feet, considering Jon lives 250 feet from Max.

To find out how many inches separate Jon's home from Max's on the map, we need to apply the given scale of the map which is 1 inch:125 feet. Since Jon lives 250 feet away from Max, we can set up a proportion to solve for the distance on the map as follows:

1 inch / 125 feet = x inches / 250 feet

Cross-multiply to solve for x:

125x = 1 * 250

125x = 250

Now, divide both sides by 125 to isolate x:

x = 250 / 125

x = 2

So, Jon's home is 2 inches from Max's on the map.

The formula for finding the circumference of a circle is [tex]c=\pi *d[/tex] (where d is the diameter). So, simply plugging in 622 mm for d and 3.14 for pi, we find that c = 622 * 3.14 = 1953.08 mm.

Answer:

y = 4x - 23

Step-by-step explanation:

To write the slope intercept form, convert the point slope form using the distributive property and inverse operations.

y + 3 = 4(x - 5)         Distributive Property

y + 3 = 4x - 20         Subtract 3 from both sides

y = 4x - 23

Answer:

y=4x-23

Step-by-step explanation:

its correct i just did the assignment on linear functions.

In order from least to greatest, it goes 4/5, 0.81, 90%

Answer:

4/5, 0.81, 90% is the answer from least to greatest.

Hope this helps :)

[tex]A=lw\Rightarrow w=\frac{A}{l}=\frac{90}{9}=10\: ft[/tex]

Answer:

10 ft

Step-by-step explanation:

Area of a rectangular room is

A = l*w

We know the area and the length

90 = 9*w

Divide by 9

90/9 = 9w/9

10 =w

The width is 10 feet

Answer:

Dan eat [tex]2\frac{2}{3}[/tex] pizzas

Step-by-step explanation:

Let

x-----> amount of pizza Jay ate

y-----> amount of pizza Dan ate

we know that

[tex]x=\frac{2}{3}[/tex] ----> equation A

[tex]y=4x[/tex] -----> equation B

substitute equation A in the equation B and solve for y

[tex]y=4(\frac{2}{3})=\frac{8}{3}[/tex]

Convert to mixed number

[tex]\frac{8}{3}=\frac{6}{3}+\frac{2}{3}=2\frac{2}{3}[/tex]

To find the amount Dan ate, we multiply the amount Jay ate (2/3) by 4, giving us 8/3, which is also known as 2 2/3 pizzas.

Jay ate 2/3 of a pizza. Dan ate 4 times the amount that Jay ate. To find out how much Dan ate, we need to multiply the fraction of the pizza that Jay ate by 4.

So, Dan ate 4 x (2/3) = 8/3 pizzas. Since 8/3 is greater than the whole, it can also be represented as 2 2/3 pizzas.

Answer:

c) 8

Step-by-step explanation:

its C. because 17-9=8.

Answer:

0.01.

113.

Step-by-step explanation:

Probability of a defect = 9/1200

= 0.0075

= 0.01 to the nearest hundredth.

Prediction  of number of defects in 15,000 computers

= 15,000 * 0.0075

=  113.

The probability of choosing defective computers is 0.01 and the number of predictions is 113.

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favorable outcomes / Number of samples

Given that manufacturer tests 1200 computers and finds that 9 of them have defects. Find the probability that a computer chosen at random has a defect.

The probability will be calculated as,

Probability of a defect = 9/1200

= 0.0075

= 0.01 to the nearest hundredth.

Prediction  of the number of defects in 15,000 computers

= 15,000 * 0.0075

=  113.

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Answer:

[tex]x=35\°[/tex]

Step-by-step explanation:

we know that

In a quadrilateral inscribed in a circle , the opposite angles are supplementary

so

In this problem

[tex](3x+2)\°+(3x-32)\°=180\°[/tex]

Solve for x

[tex]6x-30\°=180\°[/tex]

[tex]6x=210\°[/tex]

[tex]x=210\°/6=35\°[/tex]

Answer:

A. 35

Step-by-step explanation:

I did this question earlier and A. 35 was the answer that was right for me. Hope this helps!

Answer:

9.9

Step-by-step explanation:

First, you divide the 33 by 8 because that's the first part that goes together.

33/8=4.125

Second, divide 12 by 5.

12/5=2.4

Then, you multiply the 4.125 and the 2.4 together.

4.125 x 2.4 = 9.9

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➷To multiply a fraction, you can just multiply the top and multiply the bottom.

Top: 33 * 12 = 396

Bottom: 8 * 5 = 40

Fraction: 396/40

Simplify: 28 2/7

Or in decimal form: 9.9

Final answer:

33/8 * 12/5 = 28 2/7

✽

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TROLLER

Answer:

28.27 inches for inner and 36.12 inches for outer

Step-by-step explanation:

2[tex]\pi[/tex]r

and 2 pi r with 4.5 +2.5 inches as the radius.

You're done :-)

90-37=53 complementary angles are 90 degrees

Answer:

Option A, 53°

Step-by-step explanation:

If the two angles are complimentary to each other then sum of these angles is equal to 90°.

∠AOB + ∠AOC = 90°

If ∠AOC = 37°

Then ∠AOB = 90° - ∠AOC

                     = 90° - 37°

                     = 53°

Option A 53° is the answer.

It means f(x) has a set of numbers from 0-2

i.e, 0,1,2

Answer:

A: -6

Step-by-step explanation:

A direct variation is y =kx

We know x =4 and y = -24

Substituting in

-24 = 4k

Dividing by 4

-24/4 = 4k/4

-6 =k

The constant of variation is -6

Answer:

a. [tex]x=-1,3,\:or\:6[/tex]

Step-by-step explanation:

The given equation is;

[tex]x^3-8x^2+9x+18=0[/tex]

To solve by the x-intercept method we need to graph the corresponding function using a graphing calculator or software.

The corresponding function is

[tex]f(x)=x^3-8x^2+9x+18[/tex]

The solution to [tex]x^3-8x^2+9x+18=0[/tex] is where the graph touches the x-axis.

We can see from the graph  that; the x-intercepts are;

(-1,0),(3,0) and (6,0).

Therefore the real solutions are:

[tex]x=-1,3,\:or\:6[/tex]

Answer:

Use a graphing utility or a graphing calculator.

x = -1, 3, 6.   (3 real solutions).

Step-by-step explanation:

The points of intersection on the x axis are the 3 solutions to the equation.

Answer:

the cost of each charm

Step-by-step explanation:

Since x is the number of charms and it is multiplied by 25, 25 is the cost of each charm

The vector parametric equation for the line segment CC is <4,0> + t<-4,5>. The line integral of F⃗  along CC is 20. The line integral of F⃗  around the clockwise-oriented triangle with corners at the origin, P, and Q cannot be determined without additional information.

(a) To find a vector parametric equation for the line segment CC, we can use the points P=(4,0) and Q=(0,5). We can represent the line segment CC as r(t) = <4,0> + t<-4,5>, where t is the parameter. This equation represents the line segment from P to Q, with t=0 corresponding to P and t=1 corresponding to Q.

(b) Using the parametrization in part (a), we can evaluate the line integral of F⃗  along CC. The line integral is given by ∫CF⃗ ⋅ dr⃗ = ∫baF⃗ (r⃗ (t))⋅r⃗ ′(t)dt. In this case, the line integral is ∫01-5yi⃗ +4xj⃗⋅-4i⃗ +5j⃗ dt

(c) Evaluating the line integral from part (b), we get 20.

(d) The line integral of F⃗  around the clockwise-oriented triangle with corners at the origin, P, and Q can be found using the Green's theorem. We can calculate it by subtracting the line integral along CP from the line integral along CQ. However, we would need more information to determine the path from C to the origin.

Answer:

Option 1 - [tex]x\approx 1.58[/tex]

Step-by-step explanation:

Given : Exponential equation [tex]17^x=89[/tex]

To find : Solve exponential equation by using properties of common logarithms?

Solution :

Step 1 - Write the exponential equation,

[tex]17^x=89[/tex]

Step 2 - Take logarithm both side,

[tex]\log 17^x=\log 89[/tex]

Step 3 - Apply logarithmic property, [tex]\log a^x=x\log a[/tex]

[tex]x\log 17=\log 89[/tex]

Step 4 - Divide both side by log 17,

[tex]x=\frac{\log 89}{\log 17}[/tex]

Step 5 - Solve,

[tex]x=1.584[/tex]

[tex]x\approx 1.58[/tex]

Therefore, Option 1 is correct.

Answer:

find the perimeter and multiply it to a decent size to see what you would need to do to enlarge the map

Step-by-step explanation:

can i get brainliest i need 5

The area of the enlarged map is gotten by multiplying the square of the scale factor by 21 in²

Scaling is the increase or decrease in the size of a figure by a scale factor so as to create an image.

If a map is enlarged by a scale factor. To determine the area of the enlarged map, if the original map has an area of 21 in²:

Area of enlarged map = scale factor² * 21 in²

The area of the enlarged map is gotten by multiplying the square of the scale factor by 21 in²

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Answer:

The original price of the shirt is $36.

Step-by-step explanation:

Let us call p_o the original price of the shirt, then we know that $14.40 is 60% off [tex]p_o[/tex]; or $14.40 is 100% - 60% = 40% of [tex]p_o[/tex]. In other words,

[tex]\dfrac{40\%}{100\%}*p_o= \$ 14.40.[/tex]

This equation simplifies to

[tex]0.4p_o= \$14.40[/tex]           (we evaluated 40/100 )

We divide both sides by 0.4 and get:

[tex]p_o= \dfrac{\$14.40}{0.4}[/tex]

[tex]\boxed{p_o = \$36.}[/tex]

The original rice of the shirt is $36.

Answer:

$36

Step-by-step explanation:

If the shirt is 60% off, it is currently .4 of the original price. Thus the original price was: $36

Hope this helped! :)

Answer: 48°

Step-by-step explanation: The Answer is 48° this is because a triangle is equal to 180° and to find the missing side, add the two sides you do know and subtract them from 180 and you will get 48°

Have an awesome day,

Eric

Answer:

$8.608

Step-by-step explanation:

We are given that it costs $2.69 per pound to ship a package and we are to find how much would it cost to ship a package weighing 3.2 lbs.

To find this, we simply need to multiply the unit cost per pound with the weight of the package that is to be shipped.

Total cost to ship 3.2 lbs package = [tex] 3.2 \times 2.69 [/tex] = $8.608

Answer:

AAA (Or even just two angles work too, since the last has to be the same no matter what) ASA and SSS

Step-by-step explanation:

I believe this is the same as before? As far as I know these are the main rules for proving similarity. (AAS and A** do not exist (Brainly won't let me say the two Ss), make sure no trick questions get you ;p)

I'm not sure if what you needed earlier was the relationships between angles to find them? Like to find Exterior Angles subtract <C from 180 = <EA?

Answer:

C x=17

Step-by-step explanation:

The top and bottom sides have to be equal for the quadrilateral to be a parallelogram

2x-9 = x+8

Subtract x from each side

2x-9-x = x+8-x

x-9 = 8

Add 9 to each side

x-9+9=8+9

x=17

➷ Opposite lengths in a parallelogram are equal

Therefore:

2x - 9 = x + 8

Add 9 to both sides:

2x = x + 17

Subtract x from both sides:

x = 17

Your answer is option c.

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Answer:

[tex]30-3d\leq 20[/tex]

Step by step explanation:

Let d represent the rate of temperature decrease in degrees Celsius per day from Monday to Thursday.  

As temperature decreased at a constant rate in the next 3 days, so the rate of temperature will decrease 3d degree Celsius in 3 days.  

We are told that the pool was open on Monday. The high temperature was [tex]30^{\circ}{\text{C}[/tex] on Monday. So the decrease in temperature from Monday to Thursday will be [tex]30-3d[/tex].

We have been given that the swimming pool is open when the high temperature is higher than [tex]20^{\circ}{\text{C}[/tex].

As the pool was closed on Thursday. This means that temperature on Thursday was less than or equal to 20 degree Celsius. We can represent this information in an inequality as:

[tex]30-3d\leq 20[/tex]

Therefore, the inequality [tex]30-3d\leq 20[/tex] can be used to determine the rate of temperature decrease in degrees Celsius per day, d, from Monday to Thursday.

Answer:

30-3d=20

Step-by-step explanation:

Trust me i got it correct

hope im right but i think it 1 sorry if im wrong

Plug in 1, 2, 3, ... up to 8 into our sequence an.

You really just need to plug in 8, but plug in lower numbers to see the sequence emerge.

For example:

a1 means n equals 1, so a1 = 25 - (3 * 1) = 25 - 3 = 22

a2 means n equals 2, so a2 = 25 - (3 * 2) = 25 - 6 = 19

...

a8 means n equals 8, so a8 = 25 - (3 * 8) = 25 - 24 = 1

I hope this helps you understand the problem.

EDIT: You can also graph your iterative rule an on a graph. The values on the x axis correspond to the value of n and the y-axis would then correspond to the value of the sequence. Notice that a8 = 1, as shown in the attached picture.

Answer with explanation:

  The equation whose equivalent equation we have to find is:

        5 √X +8=35

Two equations are said to be equivalent,if they have same solution .

There is another definition of equivalent equation.Two equation are said to be equivalent ,also, if their solution are not same, but these equations appear Identical that is congruent but not Similar.

Option A: Equation ,3√X +8=175 is equivalent to 5√X+8=35.

Answer:

A

Step-by-step explanation

For this case, we find the equation of the line, for this we look for points where the line passes:

[tex](x1, y1) = (- 2,0)\\(x2, y2) = (- 10, -4)[/tex]

We found the slope:

[tex]m = \frac {y2-y1} {x2-x1} = \frac {-4-0} {- 10 - (- 2)} = \frac {-4} {- 10 + 2} = \frac {- 4} {- 8} = \frac {1} {2}[/tex]

Thus, the equation of the line is:

[tex]y = \frac {1} {2} x + b[/tex]

We substitute a point to find "b":

[tex]0 = \frac {1} {2} (- 2) + b\\0 = -1 + b\\b = 1[/tex]

Finally:

[tex]y = \frac {1} {2} x + 1[/tex]

Now, the domain is given by all the values for which the function is defined.

It is observed that "x" can take any value, that is, it is defined for all real numbers.

Answer:

Option A