If 3.78 liters of cranberry juice costs $6.95, then how much will Niki pay for 7.56 L?

To find the value of Az in the geometric sequence, we can use the given information. The geometric sequence is represented as follows: A3, 60, 160, 06 = 9.

From this, we can see that the third term (A3) is 60 and the common ratio (r) is 160/60.

To find Az, we need to determine the value of the nth term in the sequence. In this case, we are looking for the term with the value 9.

We can use the formula for the nth term of a geometric sequence:

An = A1 * r^(n-1)

In this formula, An represents the nth term, A1 is the first term, r is the common ratio, and n is the position of the term we are trying to find.

Since we know A3 and the common ratio, we can substitute these values into the formula:

60 =\(A1 * (160/60)^(3-1)\)

Simplifying this equation, we have:

\(60 = A1 * (8/3)^260 = A1 * (64/9)\)

To isolate A1, we divide both sides of the equation by (64/9):

A1 = 60 / (64/9)

Simplifying further, we have:

A1 = 540/64 = 67.5/8.

Therefore, the first term of the sequence (A1) is 67.5/8.

Now that we know A1 and the common ratio, we can find Az using the formula:

Az = A1 * r^(z-1)

Substituting the values, we have:

Az =\((67.5/8) * (160/60)^(z-1)\)

However, we now have the formula to calculate it once we know the position z in the sequence.

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Answer:

The choice A .

\( \frac{3}{7} (2x + 5)\)

Step-by-step explanation:

\(a. \: \frac{3}{7} (2x + 5) = \frac{6}{7} x + \frac{15}{7} = \frac{6}{7}x + 2 \frac{1}{7} \\ \\ \\ b. \: \frac{1}{7} (6x + 2) = \frac{6}{7} x + \frac{2}{7} \\ \\ \\ c. \: \frac{2}{7} (3x + 4) = \frac{6}{7} x + \frac{8}{7} = \frac{6}{7} x + 1 \frac{1}{7} \\ \\ \\ d. \: \frac{6}{7} (x + 1 \frac{2}{7} ) = \frac{6}{7} (x + \frac{9}{7} ) = \frac{6}{7} x + \frac{54}{49} \)

(-3, 3) and (4, -1) are the points that can be used to form a right triangle to derive the distance formula to find the length of the line segment

Given the line on the xy-plane, we are to determine the points on the line that can be used to determine the distance between the two points.

The required points on the line will be the two endpoints on the line. The end points are (-3, 3) and (4, -1). The distance between this points is expressed as:

D = √(-1-3)²+(4+3)²
D = √14 + 49
D = √63

Hence the points that can be used to form a right triangle to derive the distance formula are (-3, 3) and (4, -1)

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Answer: It’s -1,-3

Step-by-step explanation:

got 100 on the test

Answer:

D. 75

Step-by-step explanation:

To find the possible number of teachers at the meeting, find which answer choice creates a whole number answer when calculating the 40% of teachers that are male and the 20% of them that teach math.

This number is answer choice D, 75.

40% of 75 is 30.

Of those 30 teachers, 20% of 30 is 6.

So, since each quantity is a whole number, this could be the possible number of teachers at the meeting.

The correct answer is D. 75

Answer:

a) You will reach 9 meters above the pool.

b) The length of time you are in the air is 2 seconds.

c) The height of the diving board is 7 meters.

Step-by-step explanation:

Given quadratic equation:

\(m(d)=-4d^2 + 5.5d + 7\)

To determine how far above the pool you reach on your dive, find the y-value of the vertex of the given quadratic equation.

The formula for the x-value of the vertex is -b/2a for a quadratic equation in the form y=ax²+bx+c.  Therefore, the x-value of the vertex for the given equation is:

\(\implies -\dfrac{5.5}{2(-4)}=0.6875\)

To find the y-value of the vertex, substitute d = 0.6875 into the given equation:

\(\begin{aligned}m(0.6875)&=-4(0.6875)^2+5.5(0.6875)+7\\&=-1.890625+3.78125+7\\&=1.890625+7\\&=8.890625\\&=9\; \sf m\;(nearest\;meter)\end{aligned}\)

Therefore, you will reach 9 meters above the pool (rounded to the nearest meter).

You will hit the water when your height is zero. Therefore, to find the length of time you are in the air, set the given quadratic equation to zero and solve for d using the quadratic formula.

\(\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}\)

\(\implies d=\dfrac{-5.5 \pm \sqrt{5.5^2-4(-4)(7)}}{2(-4)}\)

\(\implies d=\dfrac{-5.5 \pm \sqrt{142.25}}{-8}\)

\(\implies d=\dfrac{-5.5 \pm \sqrt{142.25}}{-8}\)

\(\implies d=-0.803357..., \;2.178357...\)

As time is positive we can discount the negative solution. Therefore, the length of time you are in the air is 2 seconds (rounded to the nearest second).

The height of the diving board is the y-intercept of the graph of the equation. The y-intercept is the value of y when x = 0. Therefore, to find the height of the diving board, substitute d = 0 into the equation.

\(\begin{aligned}\implies d(0)&=-4(0)^2+5.5(0)+7\\&=0+0+7\\&=7\end{aligned}\)

Therefore, the height of the diving board is 7 meters.

The answer is (B) 18.

In order to calculate the area of a triangle we must use the equation 1/2·base·height.

In this case, the base of the triangle would be QR, which is 12. The height would be PH, which is 3.

Using the formula above, we can do 1/2·12·3 which equals 18. This is the area of triangle PQR and our final answer.

Hope this helps.

The correct expression for P(X = k) will be \(P(X = k) = \binom{k-1}{r-1} \left(\frac{1}{2}\right)^k\)

Given,

The geometric distribution arises as the distribution of the number of times we flip a coin until it comes up heads. consider now the distribution of the number of flips until the -th head appears, where each coin flip comes up heads independently with probability.

The negative binomial distribution describes the probability of getting the -th success (in this case, heads) on the th trial, given a probability p of success on each trial.

We can write this as:

\(P(X = k) = \binom{k-1}{r-1} p^r (1-p)^{k-r}\)

where k is the number of flips needed to get r successes, including the rth success.

In this case, we want the distribution of the number of flips until the rth head appears,

so we can set p = 1/2,

since the coin is fair.

We also need to adjust the formula to count the number of flips, including the flip with the rth head.

Since we need r heads to appear, the last head must appear on the rth flip, so we can write:

\(P(X = k) = \binom{k-1}{r-1} \left(\frac{1}{2}\right)^r \left(\frac{1}{2}\right)^{k-r+1}\)

Simplifying the expression,

we get:

\(P(X = k) = \binom{k-1}{r-1} \left(\frac{1}{2}\right)^k\)

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Answer:

Step-by-step explanation:

Begin by squaring both sides to get rid of the radical. Doing that gives you:

\(sin^2x=1-cosx\)

Now use the Pythagorean identity that says

\(sin^2x =1-cos^2x\) and make the replacement:

\(1-cos^2x=1-cosx\). Now move everything over to one side of the equals sign and set it equal to 0 so you can factor:

\(1-cos^2x+cosx-1=0\) and then simplify to

\(cosx-cos^2x=0\)

Factor out the common cos(x) to get

\(cosx(1-cosx)=0\) and there you have your 2 trig equations:

cos(x) = 0 and 1 - cos(x) = 0

The first one is easy enough to solve. Look on the unit circle and see where, one time around, where the cos of an angle is equal to 0. That occurs at

\(x=\frac{\pi }{2},\frac{3\pi}{2}\)

The second equation simplifies to

cos(x) = 1

Again, look to the unit circle and find where the cos of an angle is equal to 1. That occurs at π only.

So, in the end, your 3 solutions are

\(x=\frac{\pi}{2},\pi,\frac{3\pi}{2}\)

Answer:

\(\frac{x}{x+2}+\frac1x=1\\\rightarrow \frac{x^2+(x+2)}{(x^2+2x}=1\\\rightarrowx^2+x+2=x^2+2x\\\rightarrowx+2=2x\\\rightarrow x=\boxed2\)

Only one solution, which is two. The answer should be C. You could obviously see that if there is no squaring then there will be no extraneous solutions.

The distance would be 315 feet which is a certain distance the front wheel gets 10 revolutions more than the back wheel.

The Circumference of a circle is defined as the product of the diameter of the circle and pi.

C = πd

where 'd' is the diameter of the circle

Given that the circumference of the back wheel=9 feet, the front wheel=7 feet. At a certain distance, the front wheel gets 10 revolutions more than the back wheel.

Both wheels must move at the same distance. If the number of revolutions taken by the back wheel is x, then the number of revolutions taken by the front wheel is x+10.

Because the distance traveled is the same as:

⇒ 9x = 7(x+10)

⇒ 9x = 7x+70

⇒ 9x - 7x = 70

⇒ 2x = 70

⇒ x = 35

We obtain x = 35 revolutions.

So the total distance traveled is 35×9=315 feet or 45×7=315 feet.

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The area of triangle ADE is,

⇒ A = 48 square units

We have to given that,

In the diagram , DE is a midsegment of triangle ABC.

And, The area of triangle ABC is 96 square units

Now, We know that,

Since DE is a midsegment of triangle ABC, it is parallel to AB and half the length of AB. Therefore, DE is half the length of AB.

Hence, the area of triangle ADE is half the area of triangle ABC,

That is,

A = 96 / 2

A = 48 square units

Thus, The area of triangle ADE is,

⇒ A = 48 square units

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Step-by-step explanation:

Given: To make smallest 3-digit number of 825.

To find: The smallest 3-digit number of 825.

Solution: We can make the smallest 3-digit number of 825 by separating the numbers and arranging it to ascending order. The given number is 825. ...

Final answer: The smallest 3-digit number of 825 is 258.

hope it helps

Answer:

258

Step-by-step explanation:

We are given 3 numbers:

8 2 5

And we are asked to find the smallest 3 digit number using those 3 digits above.

To make the smallest number, place the numbers in value from least to greatest:

2 5 8

This is your 3 digit number: 258.

Hope this helps! :)

Answer:

Step-by-step explanation:

a, e, f

Answer:

\(\huge\boxed{\sf k =3}\)

Step-by-step explanation:

Graph shows that:

y ∝ x (y is directly proportional to x)

Changing proportionality into equality

y = kx  ------------(1)

Where k is the constant of proportionality

From the graph, we have y = 6 when x = 2

Putting this in Eq. (1)

6 = k(2)

Divide both sides by 2

3 = k

OR

k = 3

\(\rule[225]{225}{2}\)

Hope this helped!

Answer:

\(\large{\pink{ \underline { \underline{ \red{ \boxed{ \blue{ \sf{k = 3}}}}}}}}\)

Answer:

θ= 150°

Step-by-step explanation:

Look at the picture below

The linear equation for the 24 is less than m is 24 = m - 8 here m is the number.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that a linear equation in one variable:

24 is less than m:

Here m is the number:

24 = m - 8

Where m is the number.

Thus, the linear equation for the 24 is less than m is 24 = m - 8 where m is the number.

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Answer:

                                                                      250

                                                                     /       \

                                                   126            124

                                                           \        /     \

                 102                      24                87       57

                /     \                 /     \       /     \

             100     6          22     2          40     17

            /     /   \       /     /   \       /     /   \

         95     0     5      22     0      20     0      37

The frequency tree shows that 126 people arrived late, and 102 of them travelled by train. This means that 24 people arrived late and travelled by bus. There were a total of 250 people who attended the conference, so 124 people arrived on time. Of the people who arrived on time, 87 travelled by bus and 57 travelled by train.

Answer:

Step-by-step explanation:

Answer:

Rounded: $478.06

Step-by-step explanation:

Set up an equation:

Variable x = original price

62/100 = 296.40/x

Cross multiply

62 × x = 100 × 296.40

62x = 29,640

Divide both sides by 62:

x = 478.064516....

Round to nearest cent (hundredths place):

x = 478.06

Check your work (using the rounded estimate will be close to $296.40 but not exact because it is rounded; once you round your answer and it should match):

478.06 × 62%

Convert the percentage into a decimal:

478.06 × 0.62

296.3972

Round to the nearest cent (hundredths place):

296.40

The nurse should administer 4 Lasix 20 mg tablets to the patient to achieve the prescribed dose of 80 mg.

To determine the number of Lasix 20 mg tablets that should be administered to the patient, we need to calculate how many tablets are equivalent to the prescribed dose of 80 mg.

Given that each Lasix tablet contains 20 mg of the medication, we can divide the prescribed dose (80 mg) by the dosage strength of each tablet (20 mg) to find the number of tablets needed.

Number of tablets = Prescribed dose / Dosage strength per tablet

Number of tablets = 80 mg / 20 mg

Number of tablets = 4 tablets

Therefore, the nurse should administer 4 Lasix 20 mg tablets to the patient to achieve the prescribed dose of 80 mg.

It is important to note that this calculation assumes that the Lasix tablets can be divided or split if necessary. However, it is crucial to follow the specific instructions provided by the prescribing physician or consult with a pharmacist if there are any concerns about the appropriate administration of the medication.

Additionally, it is important to consider any additional instructions, such as the frequency and timing of administration, as specified by the physician's order.

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Answer:

A

B

C

E

Step-by-step explanation:

Answer: A, C, E, B I think im PRETTY sure im correct. Maybe 100% sure :)

\(~~~~~~~~~~~~\textit{quadratic formula} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{2}x^2\stackrel{\stackrel{b}{\downarrow }}{-4}x\stackrel{\stackrel{c}{\downarrow }}{-7} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x= \cfrac{ - (-4) \pm \sqrt { (-4)^2 -4(2)(-7)}}{2(2)} \implies x= \cfrac{ 4 \pm \sqrt { 16 +56}}{ 4 } \\\\\\ x=\cfrac{4\pm 6\sqrt{2}}{4}\implies x=\cfrac{2\pm 3\sqrt{2}}{2}\implies x= \begin{cases} \frac{2\pm 3\sqrt{2}}{2}\\\\ -\frac{2\pm 3\sqrt{2}}{2} \end{cases}\)

The graph of the function y = log (x + 2) as required from the task content is a 2 units shift of the graph of y = log x to the left.

It follows from the task content that the graph of the logarithmic function y = log (x + 2) is to be determined.

By observation, the required graph represents a shift of the graph of y = log x to the left by 2 units.

Ultimately, the required graph is as attached.

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Answer:

Step-by-step explanation:

The smallest perfect square that has three different prime numbers as factor is 900

900 = 30 * 30

Factors = 2² * 3² * 5² = 900

The surface area of the right triangular prism is 270 sq ft

The total surface area of the prism is the  sum of all the area of its faces

For the two triangles

A = 2(0.5bh)

A = bh

A = 7 * 12 = 84 sq.ft

For the two rectangles

A = 2lw

A = 2(6*12)

A = 2 * 72 = 144 sq.ft

For the third triangle;
Area  6ft * 7ft

Area = 42 sq.feet

Taking the sum of the areas

TSA = 84 + 144 + 42

TSA  = 270 sq ft

Hence the surface area of the right triangular prism is 270 sq ft

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Answer:

Step-by-step explanation:

Assuming it has no spin

KE = ½mv²

KE = ½(12)10²

KE = 600 J

Since we want the temperature to be less than 8 degrees Fahrenheit, 8 would be the constant that Digby should use in the inequality.

what is inequality ?

An inequality is a mathematical statement that compares two values or expressions using one of the inequality symbols: "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

To write an inequality for the temperature during a winter day being less than 8 degrees Fahrenheit, we can use the inequality symbol "<" which means "less than."

So, the inequality would be:

Temperature < 8 degrees Fahrenheit

Therefore, Since we want the temperature to be less than 8 degrees Fahrenheit, 8 would be the constant that Digby should use in the inequality.

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a) The value of x is 21

b) The value of the expression is 135.

c) The value of the expression is 135.

Here we know that the lines G and M are parallel, meaning that the two shown angles are alternarte exterior angles, and thus, have the same measure, then we can write:

5*(x + 6) = 9*(x - 6)

We can solve that linear equation for x:

5x + 30 = 9x - 54

30 + 54 = 9x - 5x

84 = 4x

84/4 = x

21 = x

Then the measures of the angles are:

a1 = 5*(21 + 6) = 135°

a2 = 9*(21 - 6) = 135°

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Answer:

D

Step-by-step explanation:

its D because its saying what is greater or equal to 8 so the arrow is pointing to what larger and the it isn't negative 8 so it wouldn't pass the 0 so it would be D

Answer:

A. x\(\leq\) -3

Step-by-step explanation:

the probability that exactly 41 of 174 eligible voters aged 18-24 voted is approximately 0.7267.

How to solve?

To solve this problem using a normal approximation, we first need to calculate the mean and standard deviation of the binomial distribution, which models the number of voters among 174 eligible voters aged 18-24, given that the probability of a single eligible voter aged 18-24 voting is 0.22.

The mean of the binomial distribution is given by:

μ = np = 174 x 0.22 = 38.28

The standard deviation of the binomial distribution is given by:

σ = √(np(1-p)) = √(174 x 0.22 x 0.78) = 4.49

Next, we can use the normal distribution to approximate the probability of exactly 41 voters among 174 eligible voters. We can standardize the value of 41 using the formula:

z = (x - μ) / σ

where x is the number of voters we are interested in, μ and σ are the mean and standard deviation of the binomial distribution, and z is the standard score.

Plugging in the values, we get:

z = (41 - 38.28) / 4.49 = 0.61

We can then use a standard normal distribution table or a calculator to find the probability that a standard normal variable is less than 0.61. This probability is approximately 0.7267.

Therefore, the probability that exactly 41 of 174 eligible voters aged 18-24 voted is approximately 0.7267.

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