A random sample is taken and the sample size is 25. the sample is normally distributed, the sample mean is 80, and the standard deviation is 5.5. find a 90% confidence interval for the population mean.

Problem 10

The two functions are inverses of each other. Why? Because we can think of f(x) = (x-7)/(-2) as y = (x-7)/(-2).

Swap x and y to get x = (y-7)/(-2). Solving for y leads to y = -2x+7 showing that g(x) = -2x+7 is the inverse of f(x) = (x-7)/(-2). This process can be done in reverse to get the same result.

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Problem 11

y = a(6)^(t/2)

y = a( 6^(1/2) )^t

y = a(2.4494897)^t

y = a( b )^t

where b = 6^(1/2) = 2.4494897 approximately

Set b equal to 1+r and solve for r

1+r = 2.4494897

r = 2.4494897-1

r = 1.4494897

This rounds to about r = 1.45

The r value is the decimal form of the percentage, which means we move the decimal point over two spots to the right to get 145% approximately

Answers:

The equation is roughly y = a(1 + 1.4494897)^t

The growth rate is approximately 145%

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Problem 12

You have the correct answer. Nice work.

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Problem 13

You are very close to the correct answer. However, you're missing the base of the log.

The answer should be [tex]\log_{49}(343) = \frac{3}{2}[/tex]. So you'll need to write in a small "49" under the log.

The general rule is that exponential equations in the form [tex]b^x = y[/tex] are equivalent to the log version of [tex]\log_{b}(y) = x[/tex]. For each equation, b is the base. The idea of logs is to isolate the exponent.

Answer:

69 meters squared

Step-by-step explanation:

You can split the shape into two small rectangles by drawing a vertical line. Then, you can solve for the areas of the two rectangles separately and then add them together.

The larger rectangle would have an area of 5 * 12, or 60 m^2.
The smaller rectangle would have an area of 3 * 3, or 9 m^2.
Simply add those together and the total area would be 69 m^2.

Answer:

Area is 69 m

Step-by-step explanation:

Answer:

each teammate contributed 1.43 sorry but i do not know how many members they have because my head hurts

Answer:

The decimal 0.345 expressed as a fraction is 69200 .

Answer:

Step-by-step explanation:

Here we will show you step-by-step how to get the solution to: "What is 5/14 rounded to the nearest whole number?"

First, we convert the fraction to a decimal number by dividing the numerator by the denominator:

5 / 14 = 0.3

Then, we round to the nearest whole number using the following rules:

If the number to the right of the decimal point is .5 or higher, then add 1 to the left of the decimal point.

If the number to the right of the decimal point is less than .5, then leave the number to the left of the decimal point as is and remove the digit to the right of the decimal point.

.4 is less than .5. Thus, we leave the number to the left of the decimal point as is and remove the digit to the right of the decimal point.

5/14 rounded to the nearest whole number is therefore:

0

Answer:

Please see attachment.

The first one is a quadrilateral that is not a parallelogram.

The second one is a triangle with a right angle.

Step-by-step explanation:

Hope this helps!

If not, I am sorry.

Answer:

[tex]x = \frac{4y + 1}{3} [/tex]

The goal is to isolate the X value. So the first step would be to add 1 to both sides, making the equation 4y + 1 = 3x.

Then you divide both sides by 3, making the equation (4y + 1)/3 = x

If you have a Y value then you'd plug it in for Y and solve for x but since there isn't one provided you're done.

Answer:

45 feet

Step-by-step explanation:

if 1 cm = 3 ft, we can scale up the drawing from there.

We are multiplying each cm by 3, and considering that length to be 3 feet.

If we had 2 cm, (multiply both by 3) we would have 6 feet.

So, if we had 15 cm, we also need to convert this scale length into actual length. We do this by multiplying

15 × 3 = 45

So, we know that the actual length of the playground in feet is 45 feet.

Sum of triangle angles = 180

smallest angle = x

second angle = 3x

third angle = x +35

180 = x + 3x + x + 35

145 = 5x

x = 29 is the smallest

the second is 87

the third is 64

Step-by-step explanation:

i think b is right answer

Answer:

see photo for detailed analysis

The unit rate is the rate for one of something (Taken from HMHCO).

For instance, you could say that Bob can make 6 gift cards in 3 hours. The unit rate would be 2 gift cards per hour. We solved for this by dividing both values by 3.

3 dollars per toy

This is a unit rate. Why? Because it gives us the rate, 3 dollars, and it is for one of something, which this case would be toys.

1 toy per 5 dollars

This is not a unit rate. Why? We still get the rate, 1 toy, but this time it isn't for one of something, which in this case is dollars. It is a rate for 5 dollars, not 1 dollar.

1 toy per 5 dollars

Answer:

[tex]\mathsf {y =\frac{15}{7}x }[/tex] < [tex]\mathsf {y=\frac{13}{6}x }[/tex] < [tex]\mathsf {y=\frac{11}{5}x }[/tex] < [tex]\mathsf {y=\frac{21}{9}x }[/tex] < [tex]\mathsf {y= \frac{19}{8}x}[/tex]

Step-by-step explanation:

Finding the unit rate of the graph :

Now, the equations with greater unit rates (in increasing order) are :

The option third ∠R ≅ ∠V is correct because line segment RS and UV are parallel which is crossed by a transversal RV.

It is defined as the law to prove that the two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have given two triangles:

Triangle RST and Triangle VUT

AS we can see Line segment RS and UV are parallel.

Which is crossed by a transversal RV.

The angle SRV = Angle RVU

Thus, the option third ∠R ≅ ∠V is correct because line segment RS and UV are parallel which is crossed by a transversal RV.

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Answer:

c

Step-by-step explanation:

Answer:

[tex]\rightarrow \fbox {Yes} \leftarrow[/tex]

Step-by-step explanation:

ΔABC is a right triangle as it possesses a right angle (90°).

Triangle ABC is a right angled triangle since it holds Pythagoras theorem.

Right angled triangle are those triangle for which one of the angle is 90 degrees.

For a right angled, triangle, there is a theorem called Pythagoras Theorem which relates the three sides of the triangle.

Pythagoras theorem states that,

Hypotenuse² = Base² + Altitude²

Here AC is the hypotenuse, BC is the base and AB is the altitude.

Base² + Altitude² = (BC)² + (AB)²

                             = 5² + 12²

                             = 25 + 144

                             = 169

                             = 13²

                             = AC²

                             = Hypotenuse²

Pythagoras theorem holds for the given triangle.

Hence the given triangle ABC is a right angled triangle.

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Answer:

8 soccer balls

Step-by-step explanation:

Since the ratio of players to soccer balls is 5:2, we can conclude that:

The question asks to find how many soccer balls are needed for 20 players.

Multiply both players and soccer balls by 4, this will get:

Henceforth, 8 soccer balls are needed for 20 players.

The two equivalent equations are d₁= 2a/d₂ and d₂= 2a/d₁ , Option 2 and 5 is the right answer.

Rhombus is a quadrilateral with all the sides equal to each other.

It is given that d₁ and d₂ are the lengths of the diagonals.

and Area = a

a = (1/2) d₁ * d₂

       d₁ * d₂ = 2a

       It can be written as

        d₁= 2a/d₂

a = (1/2) d₁ * d₂

        d₂= 2a/d₁

Therefore Option 2 and 5 are the correct answer.

The options of this question are:

1.  d₁=2Ad₂

2. d₁= 2A/d₂

3. d₂= d₁/2A

4. d₁= 2A/d₂

5. d₂= 2A/d₁

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Answer:

[tex] \sqrt[4]{ {80}^{x} } [/tex]

Step-by-step explanation:

Hope it helps

Answer:

Step-by-step explanation:

a=-110

d=-102-(-110)=-102+110=8

let n be the number of terms.

74=-110+(n-1)×8

74=-110+8n-8

74+118=8n

192=8n

n=192/8=24

[tex]s=\frac{n}{2} [2a+(n-1)d]\\s=\frac{24}{2} [2(-110)+(24-1)\times8]\\=12[-220+184]\\=12(-36)\\=-432[/tex]

I thank the answer is B

Step-by-step explanation:

10

Answer:

A, C, D, E, F

Answer:

C- Yes, because it pases the vertical line test.

Step-by-step explanation:

It passes through one point exactly.

Answer:

5

Step-by-step explanation:

Given expression:

[tex]\dfrac{6^{n+2}-6^n}{6^{n+1}+6^n}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c[/tex]

[tex]\implies \dfrac{6^n6^2-6^n}{6^n6^1+6^n}[/tex]

Factor:

[tex]\implies \dfrac{6^n(6^2-1)}{6^n(6^1+1)}[/tex]

Cancel [tex]6^n[/tex] :

[tex]\implies \dfrac{(6^2-1)}{(6^1+1)}[/tex]

Simplify:

[tex]\implies \dfrac{36-1}{6+1}[/tex]

[tex]\implies \dfrac{35}{7}[/tex]

[tex]\implies 5[/tex]

Answer:

[tex]x=1[/tex]

Step-by-step explanation:

[tex]~~~~~x = \dfrac{1}{2 - \dfrac 1{2-\dfrac{1}{2-x}}}\\\\\\\implies x = \dfrac{1}{2 - \dfrac 1{\dfrac{4-2x-1}{2-x}}}\\\\\\\implies x= \dfrac{1}{2 - \dfrac{2-x}{3-2x}}\\\\\\\implies x = \dfrac{1}{\dfrac{6-4x-2+x}{3-2x}}\\\\\\\implies x = \dfrac{3-2x}{4-3x}\\\\\\\implies 4x -3x^2 = 3-2x\\\\\\\implies 3x^2 -4x +3-2x = 0\\\\\\\implies 3x^2 -6x +3 = 0\\\\\\\implies 3(x^2 -2x +1) =0\\\\\\\implies x^2 -2x +1 = 0\\\\\\\implies (x-1)^2 = 0\\\\\\\implies x -1 = 0\\\\\\\implies x = 1[/tex]

The approximate number of bacteria after 16 hours is 60 bacteria ,Option C is the right answer.

A function is a Mathematical statement which connects a dependent variable and an independent variable.

The graph shows the  the growth rate of a certain bacteria in a lab

the number of bacteria is on the y axis and

the number of hours is on the x axis

The function is continuous ,

From the graph the approximate number of bacteria after 16 hours is

60 bacteria

Therefore Option C is the right answer.

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Answer:

x° = 47°

Step-by-step explanation:

The sum of the measurements of three interior Angles in a triangle is 180°.This is known as angle sum property.Same case is here.

78°,55° and x° are interior angles here.

So,

Solving for x°,

Hence,the value of x° is 47°.

Answer:

as we know that in cricket there is use of tan while doing bating

Answer:

-3 + -2x5 / -4 + -1 = 5

(-3 + -2)* 5/ (-4-1) = 5.