Complete the equation
[tex] \sqrt{20} = \: \: \sqrt{5} [/tex]
​

Answer:

6

Step-by-step explanation:

The given function to us is ,

[tex]\rm\implies f(x)= log_a(x) [/tex]

And its value at 7 is 2 , that is ,

[tex]\rm\implies f(x)= log_a(7) =2[/tex]

Taking this ,

[tex]\rm\implies 2= log_a(7) [/tex]

In general we know that ,

[tex]\bf\to log_a b = c ,\ then \ a^c = b [/tex]

Using this , we have ,

[tex]\rm\implies a^2 = 7 [/tex]

Squarerooting both sides ,

[tex]\rm\implies a =\sqrt{ 7 }[/tex]

Therefore , when x is 343 ,

[tex]\rm\implies f(343)= log_{\sqrt7} ( 343) [/tex]

We can write , 343 as 7³ ,

[tex]\rm\implies f(343)= log_{\sqrt7}7^3 [/tex]

[tex]\rm\implies f(343)= log_{7^{\frac{1}{2}}} 7^3 [/tex]

This can be written as ,

[tex]\rm\implies f(343)= \dfrac{ 3}{\frac{1}{2}} [/tex]

[tex]\rm\implies \boxed{\blue{\rm f(343)= 6 }}[/tex]

Hence the required answer is 6.

Answer: Number 1 is 150

Step-by-step explanation: If you put 72 / 48% in your calculator, you will get your answer.

Answer:

y-intercept is (0, -21)

Step-by-step explanation:

For y-intercept, x = 0:

[tex]{ \sf{y + 11 = - 2(0 + 5)}} \\ { \sf{y + 11 = - 10}} \\ { \sf{y = - 21}}[/tex]

Answer:

BF = 16

Step-by-step explanation:

18/12 = 1.5 * 6 = 9

Since DE and BF are parallel and DB and EF are parallel, they comprise a parallelogram. This means that DB = EF

DB = EF = 9

24/1.5 = 16

DE = 16

BF = 16

The statement which can be proven true using the given theorem (congruence) is Segment BF = 16.

By the congruence theorem;

Hence, AE/EC = BF/FC.

Therefore; 12/18 = BF/24

Hence, BF = 24× 12/18

Read more on congruent triangles;

https://brainly.com/question/1675117

Answer:

48.48%

Step-by-step explanation:

Let's assume that there is a number N of women.

32% of these are smokers, then there are 0.32*N smokers

then 68% of these are non-smokers, then there are 0.68*N non-smokers.

Let's assume that the probability of having a ectopic pregnancy for a non-smoker is p (and the probability for a smoker will be 2*p)

Then the number of women with an ectopic pregnancy that are non-smokers is:

p*0.68*N

The number of women with an ectopic pregnancy that are smokers is:

2*p*0.32*N

Then the total number of women with an ectopic pregnancy will be:

p*0.68*N + 2*p*0.32*N

The percentage of women having an ectopic pregnancy that are smokers is equal to the quotient between the number of women with an ectopic pregnancy that are smokers and the total number of women with an ectopic pregnancy, all that times 100%.

The percentage is:

[tex]P = \frac{2*p*0.32*N}{p*0.68*N + 2*p*0.32*N} *100\%[/tex]

Taking p and N as common factors, we get:

[tex]P = \frac{2*p*0.32*N}{p*0.68*N + 2*p*0.32*N} *100\% = \frac{N*p}{N*p} \frac{2*0.32}{0.68 + 2*0.32} *100\%[/tex]

Then we get:

[tex]\frac{2*0.32}{0.68 + 2*0.32} *100\% = 48.48\%[/tex]

Answer:

Step-by-step explanation:

Answer:

170 students total

Step-by-step explanation:

43x2=86

86+43+31+10=170

9514 1404 393

Answer:

  B.  x^2/3^2 + y^2/4^2 = 1

Step-by-step explanation:

The graph looks like a circle, but is not. It is a unit circle scaled by a factor of 3 in the x-direction and a factor of 4 in the y-direction. Thus, its equation is ...

  (x/3)^2 +(y/4)^2 = 1

  x^2/3^2 +y^2/4^2 = 1

Answer:

Step-by-step explanation:

As,

[tex] \frac{2}{3} = \frac{2 \times 10}{3 \times 10} = \frac{20}{30} [/tex]

and,

[tex] \frac{3}{10} = \frac{3 \times 3}{10 \times 3} = \frac{9}{30} [/tex]

Answer:

1. 16%

2. The middle 95% of newborn babies weigh between 6.2 and 9 pounds.

3. 2.5%

4. Approximately 50% of newborn babies weigh more than 7.6 pounds.

5. 83.85%

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 7.6 pounds, standard deviation of 0.7 pounds

1. What percent of newborn babies weigh more than 8.3 pounds?

7.6 + 0.7 = 8.3.

So more than 1 standard deviation above the mean.

The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.

Of those above the mean, 100 - 68 = 32% are more than one standard deviation above the mean. So

[tex]0.32*0.5 = 0.16[/tex]

16% of newborn babies weigh more than 8.3 pounds.

2. The middle 95% of newborn babies weigh between and pounds.

Within 2 standard deviations of the mean, so:

7.6 - 2*0.7 = 6.2 pounds

7.6 + 2*0.7 = 9 pounds.

The middle 95% of newborn babies weigh between 6.2 and 9 pounds.

3. What percent of newborn babies weigh less than 6.2 pounds?

More than 2 standard deviations below the mean, which is 5% of the 50% below the mean, so:

[tex]p = 0.05*0.5 = 0.025[/tex]

2.5% of newborn babies weigh less than 6.2 pounds.

4. Approximately 50% of newborn babies weigh more than pounds.

Due to the symmetry of the normal distribution, the mean, so 7.6 pounds.

Approximately 50% of newborn babies weigh more than 7.6 pounds.

5. What percent of newborn babies weigh between 6.9 and 9.7 pounds?

6.9 = 7.6 - 0.7

9.7 = 7.6 + 3*0.7

Within 1 standard deviation below the mean(68% of the 50% below) and 3 standard deviations above the mean(99.7% of the 50% above). So

[tex]p = 0.68*0.5 + 0.997*0.5 = 0.8385[/tex]

83.85% of newborn babies weigh between 6.9 and 9.7 pounds.

Answer:

50?

Step-by-step explanation:

Because its 50 miles per gallon, so gallon time 50 will be the miles? I'm not sure but i think it is

Answer:

Domain -1 ≤x<2

Range 0 < y ≤4

Step-by-step explanation:

Domain is the input values

X goes from -1 to 2 ( 2 not included)

Domain -1 ≤x<2

Range is the output values

y goes from 0 ( not included) to 4

Range 0 < y ≤4

here's the answer to your question

Answer:

24

Step-by-step explanation:

Answer:

I THINK the answer is C. CA/BA = BA/CA

Nice job with part A on getting those correct answers.

====================================================

Part B

Let's calculate the z score for the raw score x = 37

z = (x - mu)/sigma

z = (37 - 43)/3

z = -6/3

z = -2

A negative z score tells us we're below the mean. Specifically, we are exactly 2 standard deviations under the mean.

If you repeat those steps for x = 46 (not changing mu or sigma), then you should get z = 1. So we're now 1 standard deviation above the mean.

Ultimately, we want to know the area under the standard normal curve (aka z curve) from z = -2 to z = 1.

Refer to the chart below which is a breakdown of the Empirical Rule. The pink areas are within 1 standard deviation of the mean. We have two regions taking up roughly 34% of the full area under the curve, so they combine to 34+34 = 68%

Then we add on another 13.5% which is the blue area on the left (between z = -2 and z = -1)

So 13.5+68 = 81.5% of the area under the curve is between z = -2 and z = 1.

Note: the percent sign is already taken care of for us, so there's no need to type it in. But the answer above of course means 81.5% and that answer is approximate.

====================================================

Part C

Let's find the z score for x = 34. The values of mu and sigma are the same as before.

z = (x - mu)/sigma

z = (34-43)/3

z = -9/3

z = -3

So computing P(X > 34) is the same as P(Z > -3)

Notice how adding up all of the values in the chart mentioned gets us:

2.35+13.5+34+34+13.5+2.35 = 99.7

which means 99.7% of the distribution is within 3 standard deviations of the mean. The remaining 100% - 99.7% = 0.3% is the combined area of both tails. So each tail is (0.3%)/2 = 0.15%

In short, 0.15% of the area under the curve is to the left of z = -3

Therefore, 100% - 0.15% = 99.85% of the widgets are going to have z values larger than -3, which in turn means they have values larger than 34.

Again you don't have to worry about the percent sign. Like before, the answer is approximate.

work and answers below

Answer:

[tex]\text{Part A.}\\(-\frac{1}{8},0),\\(\frac{3}{2},0)\\\\\text{Part B.}\\(\frac{11}{16},\frac{169}{16})\\\\\text{Part C.}[/tex]

Draw a parabola concave down with vertex at [tex](\frac{11}{16},\frac{169}{16})[/tex]. Since the leading coefficient of the equation is -16, the parabola should appear thinner than its parent function [tex]y=x^2[/tex]. Ensure that the parabola passes through the points [tex](\(-\frac{1}{8},0)[/tex] and [tex](\frac{3}{2},0)[/tex].

Step-by-step explanation:

Part A:

The x-intercepts of a function occur at [tex]y=0[/tex]. Therefore, let [tex]y=0[/tex] and solve for all values of [tex]x[/tex]:

[tex]0=-16x^2+22x+3[/tex]

The quadratic formula states that the real and nonreal solutions to a quadratic in standard form [tex]ax^2+bx+c[/tex] is equal to [tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex].

In [tex]-16x^2+22x+3[/tex], assign:

Therefore, the solutions to this quadratic are:

[tex]x=\frac{-22\pm\sqrt{22^2-4(-16)(3)}}{2(-16)},\\x=\frac{-22\pm 26}{-32},\\\begin{cases}x=\frac{-22+26}{-32}=\frac{4}{-32}=\boxed{-\frac{1}{8}},\\x=\frac{-22-26}{-32}=\frac{-48}{-32}=\boxed{\frac{3}{2}}\end{cases}[/tex]

The x-intercepts are then [tex]\boxed{(-\frac{1}{8},0)}[/tex] and [tex]\boxed{(\frac{3}{2},0)}[/tex].

Part B:

The a-term is negative and therefore the parabola is concave down. Thus, the vertex will be the maximum of the graph. The x-coordinate of the vertex of a quadratic in standard form [tex]ax^2+bx+c[/tex] is equal to [tex]x=\frac{-b}{2a}[/tex]. Using the same variables we assigned earlier, we get:

[tex]x=\frac{-22}{2(-16)}=\frac{-22}{-32}=\frac{11}{16}[/tex]

Substitute this into the equation of the parabola to get the y-value:

[tex]f(11/16)=-16(11/16)^2+22(11/16)+3,\\f(11/16)=\frac{169}{16}[/tex]

Therefore, the vertex of the parabola is located at [tex]\boxed{(\frac{11}{16},\frac{169}{16})}[/tex]

Answer:

b

Step-by-step explanation: i took this two please mark brainly

Answer:

33.00 355.2

5.0m x 6.7m 33.50 360.6

5.0m x 6.8m 34.00 366.0

5.0m x 6.9m 34.50 371.4

5.1m x 6.0m 30.60 329.4

5.1m x 6.1m 31.11 334.9

5.1m x 6.2m 31.62 340.4

5.1m x 6.3m 32.13 345.8

5.1m x 6.4m 32.64 351.3

5.1m x 6.5m 33.15 356.8

5.1m x 6.6m 33.66 362.3

5.1m x 6.7m 34.17 367.8

5.1m x 6.8m 34.68 373.3

5.1m x 6.9m 35.19 378.8

Answer:

1/5^8

Step-by-step explanation:

We know that a^b^c = a^(b*c)

(5^-2)^4

5^(2*-4)

5^-8

We know that a^-b = 1/a^b

1/5^8

Answer:

If m is parallel to n and n is perpendicular to p, then m is perpendicular to p.

Step-by-step explanation:

If you draw m parallel to n and then you run a line p through n such that n and p are perpendicular. The line p will also cross over m since lines go on forever and it will be perpendicular to m as well.

Answer:

Option C

Step-by-step explanation:

From the question we are told that:

Eccentricity [tex]e=0.203[/tex]

Minimum distance from the Sun [tex]d_s= 4.5 x 10^7 km[/tex]

Perihelion distance from a planet to the Sun is [tex]r= a(1 - e)[/tex]

Aphelion distance [tex]r'=a(1 + e)[/tex]

Generally the equation for Perihelion distance is mathematically given by

 [tex]4.5 * 10^7= a(1 - 0.203)[/tex]

 [tex]4.5 * 10^7 = 0.797a[/tex]

 [tex]a = 56.46 * 10^6 km[/tex]

Generally the equation for Aperihelion distance is mathematically given by

 [tex]r' = a(1 + e)[/tex]

 [tex]r' = 56.4617 * 10^6 (1 + 0.203)[/tex]

 [tex]r'=6.8 * 10^7 km[/tex]

Option C

Answer:

y  ≥ 5x+ (-3)

Step-by-step explanation:

greater than or equal to ≥

The sum means add

y  ≥ 5x+ (-3)

Answer:

Option D, y ≥ 5x + (-3)

Step-by-step explanation:

Step 1:  Make an expression

The value of y is greater than or equal to the sum of five times the value of x  and negative three.

The value of y is greater than or equal to ← y ≥

The sum of five times the value of x  and negative three ← 5x + (-3)

y ≥ 5x + (-3)

Answer:  Option D, y ≥ 5x + (-3)

Answer:

x=71

Step-by-step explanation:

Since this is an isosceles triangle as indicated by the lines on the sides, the sides lengths are equal.

When the sides are equal, the base angles are equal

x=71

Answer:

[tex]f(x) = \sqrt{x} - 2[/tex]

Step-by-step explanation:

The starting point of the graph starts in the negative y axis. This means we must have either a horinzontial reflection, a negative vertical stretch or compression, or a negative vertical shift.

The first option is the only sign of the starting point be negative so that is the answer.

Answer:  D) The base is e^(-1)

We use the rule that x^(-k) = 1/(x^k). That allows us to say e^(-1) = 1/(e^1) = 1/e

The 1/e is the base of the exponential (1/e)^x

In general, the exponential b^x has base b.

Answer: A=πr²      

A=3.14(1.6inch)²                     r=d/2⇒3.2/2⇒1.6

A=3.14×2.56in²

A=8.0384in²

A≈8.04

now circumference,

C=2πr

C=2×3.14×1.6in

C=10.048in

C≈10.05

9514 1404 393

Answer:

Step-by-step explanation:

The range of the function is the vertical extent. Here, the values of y can be anything that is -2 or more:

  range: -2 ≤ y

The domain of a the function is the horizontal extent. The domain of any polynomial function is ...

  domain: All reals

9514 1404 393

Answer:

  C.  3

Step-by-step explanation:

AD is perpendicular to BC, so its slope will be the opposite of the reciprocal of the slope of BC.

The slope of BC can be found from the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (-1 -2)/(3 -(-6)) = -3/9 = -1/3

Then the slope of AD is ...

  -1/(-1/3) = 3