We want to estimate the true mean number of ounces of water a high school athlete drinks each day at a 95% confidence level. A random sample of 15 athletes from a school is selected, and their typical daily water consumption is reported below:
64, 72, 80, 88, 128, 128, 128, 132, 145, 155, 160, 175, 180, 200, 225

Use the table to find the appropriate value of t* to use in the given scenario. Enter in the value of t* exactly as you see it written in the table.
t* =

Answer:

Ix + 2I - 5 = -(x - 1)*(x - 3)

Step-by-step explanation:

In the graph, we can see two functions a red one, f(x), and a blue one, g(x)

And the equation would be f(x) = g(x)

The red one is an absolute value function, we can see that the vertex is at x = -2 and at y = -5, and it has a slope equal to 1.

Remember that for an absolute value equation with a vertex (a, b) is:

f(x) = Ix - aI + b

Then in this case, the absolute value equation is:

f(x) = Ix - (-2)I - 5

f(x) = Ix + 2I - 5

The blue equation is a quadratic equation, with roots 1 and 3, and we can see that it opens down, so the leading coefficient is negative.

Remember that for a quadratic equation with roots a and b, with leading coefficient A is:

g(x) = A*(x - a)*(x - b)

Then in this case the quadratic equation is something like:

g(x) = -N*(x - 1)*(x - 3)

Then the equation will be something like:

f(x) = Ix + 2I - 5 = g(x) = -N*(x - 1)*(x - 3)

Ix + 2I - 5 = -N*(x - 1)*(x - 3)

The only option that has this shape is the first option (the top one) such that N = 1, then:

Ix + 2I - 5 = -(x - 1)*(x - 3)

is the correct option.

Answer:

Original angle = 122*

Supplementary angle = 58*

Step-by-step explanation:

A supplementary angle is one of two angles that make up 180*

If one angle is 30*, its supplementary angle is 150*. 30 + 150 = 180.

So in this case we have two angles, the original and the supplementary angle. The original angle is 64* more than the supplementary angle. The key word is MORE.

The formula to figure it out would look like this:  x + (x + 64) = 180

x is the supplementary angle

x + 64 is the original angle (64 MORE than its supplementary angle)

180 is the total measure of the two angles because they are supplementary and we know that supplementary angles always equals 180* when added together.

Take the formula and do a little algebra.

x + (x + 64) = 180

Subtract 64 from both sides

x + x = 116

Combine the x's

2x = 116

Divide both side by 2

x = 58

Remeber we know that the original angle is 64 more than the supplementary angle, so we'll add the 64 to the value of x and we get 122.

x + 64 = 122

Check our work:

x + (x + 64) = 180

58 + 58 + 64 = 180

Given :

⠀

To Find :

⠀

Solution :

Now,

⠀

According to the Question :

⠀

[tex]\longrightarrow\qquad \sf{{x + (x + 64) {}^{ \circ} = {180}^{ \circ} }}[/tex]

⠀

[tex]\longrightarrow\qquad \sf{{x + x + 64 {}^{ \circ} = {180}^{ \circ} }}[/tex]

⠀

[tex]\longrightarrow\qquad \sf{{2x + 64 {}^{ \circ} = {180}^{ \circ} }}[/tex]

⠀

[tex]\longrightarrow\qquad \sf{{2x = {180}^{ \circ} - 64 {}^{ \circ}}}[/tex]

⠀

[tex]\longrightarrow\qquad \sf{{2x = {116}^{ \circ} }}[/tex]

⠀

[tex]\longrightarrow\qquad \sf{{x = \dfrac{{116}^{ \circ}}{2} }}[/tex]

⠀

[tex]\longrightarrow\qquad \mathfrak{\pmb{{x = {58}^{ \circ} }}}[/tex]

⠀

Therefore,

⠀

Henceforth ,

Answer:

Step-by-step explanation:

hi

Answer:

70

Step-by-step explanation:

Ok so we first add 4.75 and 5.25. 4.75+5.25=10. So 10 hours each day so 10 x 7 = 70. 70 hours in 7 days

Answer:

i would say it is either 30 or 35

Step-by-step explanation:

7/2=3.5

so you would round it down to 3 or keep it that

and 4.75+5.25=10

3(10)=30 and 3.5(10)=35

If it's every two days.

Answer:

She can make [tex]\frac{33}{12}[/tex] batches.

Step-by-step explanation:

This question is solved by proportions, using a rule of three.

We have that:

For each batch of pancakes, 1/3 cups of milk are needed. Now, she has 11/12 cups of milk, so how many batches can she make?

1 batch - 1/3 cups

x batches - 11/12 cups

Applying cross multiplication:

[tex]\frac{x}{3} = \frac{11}{12}[/tex]

[tex]12x = 33[/tex]

[tex]x = \frac{33}{12}[/tex]

She can make [tex]\frac{33}{12}[/tex] batches.

Answer:2232

Step-by-step explanation:

Answer:

ADD ME ON FORtXVXVVXVXNIZZLE KE2DAEV12

Step-by-step explanation:

Answer:

Number 3

It's a cube

Step-by-step explanation:

Answer:

Nick's can travel 384 miles on a highway using a full tank of gas of his car

Step-by-step explanation:

Given

Fuel used by Nick's car = 12.5 gallon

In 12.5 gallon Nick can travel up to 240 miles

The gas tank of Nick's car can hold upto 20 gallons of fuel

With a full tank Nick can travel

[tex]\frac{240}{12.5} * 20 \\384[/tex]miles

Answer:

Step-by-step explanation:

I m sorry if i m wrong.

e no is 100% correct

Answer:

D.

Step-by-step explanation:

You pass 3x to the other side so you get 4y = -16 - 3x

to clear y you divide both sides by 4

y = (-16-3x )/ 4

you can simplify this so it so it gives us

y = -4 - 3/4x

Answer:

25%------10500

100%------x = 100 * 10500 /25 = 42000

Rta: Tenías 42000

Answer:

(x+3)(x+2)

Step-by-step explanation:

f(x)=x²+5x+6=x²+2x+3x+6=x(x+2)+3(x+2)=(x+3)(x+2)

[tex] {x}^{2} + 5x + 6[/tex]

[tex] {x}^{2} + 2x + 3x + 6[/tex]

[tex]x(x + 2) + 3(x + 2)[/tex]

[tex](x + 3)(x + 2)[/tex]

Answer:

if you are factoring the answer is 2(n-1)

if simplifying the answer is 2n-2

Step-by-step explanation:

See image below:)

Answer:

Step-by-step explanation:

The first thing to notice about this problem is that you have a mixture of Metric and English units.  The first thing that I would recommend is to convert 410 miles into Kilometers

1 mile = 1.61 km

410 miles = (410*1.61) = 660 km (rounded to the nearest km)

Now you need to know the time.  The formula for travel is d=rt.  You know the distance, and you know the rate, solve the formula for time.

t=d/r.

t=660km/120km/k

t=5.5 hours.  Plus add the 2 15 minutes breaks.  2*15=30 minutes.  60 minutes in an hour means that you add 30/60 hours to the trip, or another .5 hours.

Therefore the answer is 5.5+.5 hours.

The answer is: time=6 hours.

Answer:

23°

Step-by-step explanation:

157° = D

D + C = 180°

157 + C = 180

(group like terms)

C = 180 - 157

C= 23°

Step-by-step explanation:

1. make the denominators the same.

10/15+3/15= 13/15

Answer: 18°

Step-by-step explanation:

Complementary angles are the angles that when we add them together, the value will equal 90°.

In this question, we've to add both angles and equate them to 90°. This will be:

(2x - 4) + (5x + 17) = 90

2x - 4 + 5x + 17 = 90

Collect like terms

2x + 5x = 90 + 4 - 17

7x = 77

x = 77/7

x = 11

Angle A will be:

= (2x-4)

= 2(11) - 4

= 22 - 4

= 18°

Answer:

Step-by-step explanation:

A fraction consists of two parts the top number and the bottom one.

Think of the top number as the count and the bottom as the size indicator. So you have:

countsize indicator −−−−−−−−−−→proper names numeratordenominator

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Consider the action example of dividing 3 into 6.

We can do this division directly because their size indicators are the same. That is, we have: 61÷31. People do not normally write it this way but it is correct.

To directly divide the counts the size indicator must be the same

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So we need to see how many of 18 will fit into 34

We can not do this directly in one operation as the size indicators are not the same.

Lets make the size indicators (denominators) the same

Multiply by 1 and you do not change the value but

1 comes in many forms.

[34×1]÷18 → [34×22]÷18

[3×24×2]÷18 → 68÷18

Now that the size indicators (denominators) are the same we can just divide the counts (numerators)

countsize indicator→[68÷18]=6÷1=6

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

I could explain more showing the connection between this and the shortcut method but what I have shown you will do for now.

Answer:

6 Packs

Step-by-step explanation:

Since he needs 46 cookies, he will have to buy 46/8 which is 5.75 packs. But since the packs are sold in whole, not fractions, he buys a ceil approximation of the packs which is 6, because if he buys 5, it will not be enough.

Answer:

The height of the arch at its center is 250/9 or about 27.78 feet.

Step-by-step explanation:

We can write an equation to model the parabolic arch.

Let the left-most point of the arch be the origin (0, 0).

Since the bridge has a span of 100 feet, the right-most point must be (0, 100).

We can use the factored form of a quadratic:

[tex]y=a(x-p)(x-q)[/tex]

Where p and q are the x-intercepts.

Our x-intercepts are x = 0 and x = 100. Hence:

[tex]y=ax(x-100)[/tex]

At a point 40 feet from the center, the height of the arch is 10 feet.

The center is x = 50. So, a point 40 feet from the center can be either x = 10 or x = 90.

So, for instance, when x = 10, y = 10. Substitute and solve for a:

[tex]10=10a(10-100)[/tex]

So:

[tex]\displaystyle a=-\frac{1}{90}[/tex]

The same value will result if we let x = 90 and y = 10.

Hence, our equation is:

[tex]\displaystyle y=-\frac{1}{90}x(x-100)[/tex]

The height of the arch at its center will be when x = 50. Hence:

[tex]y(50)=\displaystyle -\frac{1}{90}(50)((50)-100)=\frac{250}{9}\approx 27.78\text{ feet}[/tex]

Answer:

[tex]B) sin(\alpha )[/tex]

Step-by-step explanation:

[tex]sin(90-0)=Cos(0)[/tex]

[tex]Cos(90-0)=sin(0)[/tex]

[tex]So...[/tex]

[tex]Cos(90-\alpha )= sin(\alpha )[/tex]

[tex]------------[/tex]

hope it helps...

have a great day!!

Answer:

cos(90°-a)

since it lies in first quadrant

sina

your option is B.sin(a)

Answer:

15.5 meters

Step-by-step explanation:

[tex]8^{\frac{4}{3}} = \sqrt[3]{8^4} = \sqrt[3]{(2^3)^4} = \sqrt[3]{2^{3*4}} = 2^4 = 16[/tex]

Answer: C (16).

[tex]2\sqrt{6} - 6\sqrt{54} = 2\sqrt{6} - 2 * 3 * \sqrt{6} * \sqrt{9} = 2\sqrt{6}(1-3\sqrt{9}) = 2\sqrt{6}(1-3*3) = 2\sqrt{6}(1-9)=2*\sqrt{6}*(-8) = -16\sqrt{6}[/tex]

1.

[tex] \sqrt[3]{8^{4} } [/tex]

2.

[tex]2 \sqrt{6} - 6 \sqrt{54} \\ 2 \sqrt{6} - 6 \sqrt{9 \times 6} \\ 2 \sqrt{6} - 18 \sqrt{6} \\ - 16 \sqrt{6} [/tex]

Answer:

25^2 = 20^2 + x^2

x^2 = 225

x = 15

Answer:

b

Step-by-step explanation:

The tangent- secant angle 55° is equal to half the difference of its intercepted arcs, that is

[tex]\frac{1}{2}[/tex] (170 - x) = 55 ( multiply both sides by 2 to clear the fraction )

170 - x = 110 ( subtract 170 from both sides )

- x = - 60 ( multiply both sides by - 1 )

x = 60 → b

Given:

The expression is:

[tex]\dfrac{2.1\times 10^6}{7\times 10^3}[/tex]

To find:

The simplified form of the given expression in standard form.

Solution:

We have,

[tex]\dfrac{2.1\times 10^6}{7\times 10^3}[/tex]

It can be written as:

[tex]\dfrac{2.1\times 10^6}{7\times 10^3}=\dfrac{21\times 10^5}{7\times 10^3}[/tex]

[tex]\dfrac{2.1\times 10^6}{7\times 10^3}=\dfrac{21}{7}\times \dfrac{10^5}{10^3}[/tex]

[tex]\dfrac{2.1\times 10^6}{7\times 10^3}=3\times 10^{5-3}[/tex]        [tex][\because \dfrac{a^m}{a^n}=a^{m-n}][/tex]

[tex]\dfrac{2.1\times 10^6}{7\times 10^3}=3\times 10^2[/tex]

Therefore, the required value is [tex]3\times 10^2[/tex].