The table represents a quadratic function C(t).


t C(t)
−2 1
−1 4
0 5
1 4
2 1

What is the equation of C(t)?
C(t) = −(x − 5)2
C(t) = (x − 5)2
C(t) = −x2 + 5
C(t) = x2 + 5

9514 1404 393

Answer:

  i. 0

  ii. 5, 9

  iii. 12

  iv. 0

Step-by-step explanation:

i. Roots are found where the numerator is zero, at x=0.

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ii. Vertical asymptotes are found where the denominator is zero, at x=5 and x=9.

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iii. The horizontal asymptote is the value of g(x) when x approaches infinity. It is the quotient of the leading terms of the numerator and denominator:

  y = (12x²)/(x²) = 12

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iv. The y-intercept is the function value when x=0.

  g(0) = 12·0/45 = 0

Answer:

A) 32 cm

Step-by-step explanation:

the rectangle could be 12cm x 4cm, giving an area of 48 sq cm

and a perimeter of 24+8 or 32 cm

Answer:

11-16 is the range

Step-by-step explanation:

Answer:

b.  The range only includes numbers greater than or equal to 0.

Step-by-step explanation:

Any square of a number will never lead to a negative number

The range of an equation is it's numerical possibilities for y

Since a square of a negative number never leads to a negative y

The answer is therefore, the range can only be zero and above

(otherwise the roots would be imaginary)

Answer:

48

Step-by-step explanation:

Answer:

a. Z = 1.99

b. 97.67%

c. Z = 2.56

d. 0.52%

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

a. If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)?

The heights of adult men in America are normally distributed, with a mean of 69.7 inches and a standard deviation of 2.66 inches, and thus, we have [tex]\mu = 69.7, \sigma = 2.66[/tex]

6 feet 3 inches = 6*12 + 3 = 75 inches, which means that we have to find z when X = 75. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{75 - 69.7}{2.66}[/tex]

[tex]Z = 1.99[/tex]

b. What percentage of men are SHORTER than 6 feet 3 inches?

The proportion is the p-value of Z = 1.99.

Looking at the z-table, Z = 1.99 has a p-value of 0.9767.

0.9767*100% = 97.67%, which is the answer.

c. If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)?

The heights of adult women in America are also normally distributed, but with a mean of 64.5 inches and a standard deviation of 2.54 inches, and thus, we have [tex]\mu = 64.5, \sigma = 2.54[/tex]. We have to find Z when X = 5*12 + 11 = 71. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{71 - 64.5}{2.54}[/tex]

[tex]Z = 2.56[/tex]

d. What percentage of women are TALLER than 5 feet 11 inches?

The proportion is 1 subtracted by the p-value of Z = 2.56.

Looking at the z-table, Z = 2.56 has a p-value of 0.9948.

1 - 0.9948 = 0.0052

0.0052*100% = 0.52%, which is the answer.

Answer:

the answers would be A, D, E

Answer:

6

Step-by-step explanation:

its a right angle so to find a side use a Pythagorean theorem

Pythagorean theorem =

[tex]a^2+b^2=c^2[/tex]

[tex]a^2+b^2[/tex] are the sides

[tex]c^2[/tex] is the hypotenuse

In this case we need the hypotenuse

[tex]3\sqrt{3} ^2 + 3^2 = c^2[/tex]

[tex]27 + 9=c^2[/tex]

[tex]36=c^2[/tex]

the opposite of squaring is square rooting so:

[tex]\sqrt{36} =6[/tex]

therefore the answer is 6 ^-^

Answer:

The ratio that compares the diameter of the first circle to the diameter of the second circle is [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Circumference of a circle:

The circumference of a circle of diameter d is given by:

[tex]C = \pi d[/tex]

In which d is the diameter.

One circle has a circumference half as large as that of a second circle.

We have that:

[tex]C_1 = \frac{C_2}{2}[/tex]

So

[tex]\pi d_1 = \frac{\pi d_2}{2}[/tex]

Simplifying by [tex]\pi[/tex]

[tex]d_1 = \frac{d_2}{2}[/tex]

[tex]\frac{d_1}{d_2} = \frac{1}{2}[/tex]

The ratio that compares the diameter of the first circle to the diameter of the second circle is [tex]\frac{1}{2}[/tex]

56

its mutiplying by 4

Amount of pounds that Ben get back is £75.

Exchange rate is defined as the value of a currency with respect to another currency in order to convert the currency.

Ben changes £800 to Euros before he goes on holiday.

Before holiday, exchange rate is, £1 = 1.25 Euro

£800 = 800 × 1.25 Euros = 1000 Euros

He spends 895 Euros.

Euros left = 1000 - 895 = 105 Euros

Now, the exchange rate is £1 = 1.40 Euro.

or 1.40 Euro = £1

⇒ 1 Euro = £ 1/1.40

⇒ 105 Euros = £ (1/1.40) × 105 = £75

Hence Ben got £75 of pounds back.

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Slope form -

y - y1 = m(x - x1)

y - 0 = -5(x - 1)

y = -5x + 5

Answer:

Step-by-step explanation:

you add all them up

Answer:

C.

Step-by-step explanation:

there is a measuement of 12 cm missing.

Just multiply all the sides!

Answer:

A. 8.0 inches

you will have to use the formula A= 2(LW + LH + WL)

Answer:

[tex]t_{n-1,\alpha/2}=3.59114678[/tex]

Therefore we do not have sufficient evidence at [tex]1\%[/tex] level that the true mean diameter has moved away from the target

Step-by-step explanation:

From the question we are told that:

Sample size [tex]n=36[/tex]

Mean diameter [tex]\=x=1.4[/tex]

Standard deviation [tex]\sigma=0.5cm[/tex]

Null hypothesis [tex]H_0 \mu=1.5[/tex]

Alternative hypothesis [tex]\mu \neq 1.5[/tex]

Significance level [tex]1\%=0.001[/tex]

Generally the equation for test statistics is mathematically given by

[tex]t=\frac{\=x-\mu}{\frac{s}{\sqrt{n} } }[/tex]

[tex]t=\frac{1.4-1.5}{\frac{0.5}{\sqrt{36} } }[/tex]

[tex]t=-1.2[/tex]

Therefore since this is a two tailed test

[tex]t_{n-1,\alpha/2}[/tex]

 Where

   [tex]n-1=36-1=>35[/tex]

   [tex]\alpha=/2=0.001/2=>0.0005[/tex]

From table

[tex]t_{n-1,\alpha/2}=3.59114678[/tex]

Therefore we do not have sufficient evidence at [tex]1\%[/tex] level that the true mean diameter has moved away from the target

Answer:

Q 3/10    R 4/25    S 3/50  T 12/25

Step-by-step explanation:

Q 15/50    3/10

R 8/50     4/25

S 3/50    3/50

T 24/ 50   12/25

Answer:

Q = 30%

R = 16%

S = 6%

T = 48%

Step-by-step explanation:

please mark this answer as brainliest

Answer:

A: the forest is at this moment being threatened by severe weather

Step-by-step explanation:

If the mean of 100 nummerical observations is 51.82 then the value of all 100 numbers is 5182.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given that mean of 100 nummerical observations is 51.82

We need to find the sum of all the observations

The formula to find mean is mean=Sum of observations/ Number of observation

From given mean=51.82

Number of observations =100

Let us take x as sum of all 100 numbers

So 51.82=x/100

Now apply cross multiplication

x=51.82×100

x=5182

Hence, if the mean of 100 nummerical observations is 51.82 then the value of all 100 numbers is 5182.

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Answer:

no

yes

yes

0.92 cents

4.72

9.26

Step-by-step explanation:

Initial value C is 1.9, Decay factor =0.41 and Growth factor = 0.59 when the function f(x)=1.9(0.41)ˣ.

Given that,

The equation f(x)=1.9(0.41)ˣ.

We have to state the initial value C, the growth or decay factor a, and percent change R for each unit increase in x.

We know that,

In order to translate their graphs over the 2D coordinate plane, I will offer the vertex form of an exponential equation for both the growth and decay functions.

In the case of growth, f(x) = a(1+r[tex])^{x-h}[/tex]+k, where b = 1+r

Decay is defined as f(x)=a(1-r)(x-h[tex])^{x-h}[/tex]+k, where b=1-r.

Consider the function  f(x)=1.9(0.41)ˣ.

We write as

f(x)=1.9(1-0.59)ˣ

So, initial value C is 1.9

Decay factor =0.41

Growth factor = 0.59

Therefore, Initial value C is 1.9, Decay factor =0.41 and Growth factor = 0.59 when the function f(x)=1.9(0.41)ˣ.

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Answer:

A

Step-by-step explanation:

The oil painting classes lastes two hours on Saturday

9514 1404 393

Answer:

  x = 90°

  y = 30°

Step-by-step explanation:

The relevant relations are ...

Arc AB is half a circle, so is 180°. Inscribed angle C intercepts that arc, so is half its measure: x = 90°.

The angles of a triangle total 180°, so y has the value that makes the sum of angles be 180°.

  y = 180° -90° -60°

  y = 30°

_____

Additional comment

It is worth remembering that a triangle inscribed in a semicircle is a right triangle. This tells you right away that x=90°.

Answer:

6 and 1/3

Step-by-step explanation:

8 minus 1 is 7 and 7 minus 2/3 is 6 1/3. Therefore the number you started with is 6 and 1/3. Hope this helps :)

Answer:

see below

Step-by-step explanation:

number 1 goes to 769.5=B(9.5) then to 81

number 2 goes to v=90.25(9.5) then to 857.375

number 3 goes to 95=19(h) then to 5