700,000 rounded to the nearest hundred thousand

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:

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:

5

Step-by-step explanation:

5+7

Answer:

170 students total

Step-by-step explanation:

43x2=86

86+43+31+10=170

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.

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:

b

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

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]

In polar coordinate, R is the set of points

{(r, θ) | 1 < r < 5 and 0 < θ < π/2}

So the integral is

[tex]\displaystyle\iint_R\sin(x^2+y^2)\,\mathrm dA = \int_0^{\frac\pi2}\int_1^5 r\sin(r^2)\,\mathrm dr\,\mathrm d\theta[/tex]

[tex]=\displaystyle\frac\pi2\int_1^5 r\sin(r^2)\,\mathrm dr[/tex]

[tex]=\displaystyle\frac\pi4\int_1^5 2r\sin(r^2)\,\mathrm dr[/tex]

[tex]=\displaystyle\frac\pi4\int_1^{25} \sin(s)\,\mathrm ds[/tex]

(where s = r ²)

[tex]=\displaystyle-\frac\pi4\cos(s)\bigg|_1^{25}= \boxed{\dfrac\pi4 (\cos(1) - \cos(25))}[/tex]

here's the answer to your question

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

9514 1404 393

Answer:

  162 mi²

Step-by-step explanation:

The area on the map is ...

  18(1 in)²

Then the area on the ground will be ...

  18(3 mi)² = 18·9 mi² = 162 mi²

Answer:

Step-by-step explanation:

Answer:

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

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:

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:

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

Answer: Number 1 is 150

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

Answer:

24

Step-by-step explanation:

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

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:  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:

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: 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

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:

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:

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:

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.