Determine the slope of the line that contains the given points T(4,6) a V(8,7)

A) -1/2
B) 4
C) 1/4
D) -4

Answer:

  center: (2, -4); radius: 5

Step-by-step explanation:

Group x-terms and y-terms. Add the squares of half the coefficient of the linear term in each group. It can be convenient to subtract the constant, too.

  (x^2 -4x) +(y^2 +8y) = 5

  (x^2 -4x +4) +(y^2 +8x +16) = 5 + 4 + 16

  (x -2)^2 +(y +4)^2 = 5^2

Comparing this to the form of a circle centered at (h, k) with radius r, we can find the center and radius.

  (x -h)^2 +(y -k)^2 = r^2

  (h, k) = (2, -4) . . . . . the circle center

  r = 5 . . . . . . . . . . . . the radius

Answer:

Step-by-step explanation:

The trig identities are helpful for this.

  sin² θ = 1 - cos² θ = 1 -(1/6)² = 35/36

  sin θ = (√35)/6 . . . . . . take the square root

__

  tan² θ = sec² θ -1 = (1/cos² θ) -1 = 6² -1 = 35

  tan θ = √35 . . . . . . . . . take the square root

Answer:

4.97485 (approximately)

Step-by-step explanation:

You have the information SAS given.

This is a case for law of cosines.

[tex]b^2=a^2+c^2-2ac*cos(B)[/tex]

[tex]b^2=12^2+10^2-2(12)(10)*cos(24)[/tex]

[tex]b^2=144+100-240cos(24)[/tex]

[tex]b^2=244-240cos(24)[/tex]

Take the square root

[tex]b=\sqrt{244-240cos(24)}[/tex]

I was saving rounding to the end that is why I didn't put 240*cos(24) in my calculator.

So now I'm going to put sqrt(244-240*cos(24)) in my calculator. Make sure your calculator says deg (for degrees).

4.97485 (approximately)

Answer:

The given statement is true.

Step-by-step explanation:

Quadrilaterals are similar if their corresponding sides are proportional.

This statement is true.

Quadrilaterals are similar when

a) corresponding angles are equal

b) the corresponding sides are proportional i,e the ratios of corresponding sides are equal

So, the given statement is true.

Answer:

  FALSE

Step-by-step explanation:

Corresponding angles must also be congruent for the figures to be similar. Proportional sides is not a sufficient condition.

Answer:

  A.  Y = -6X + 9

Step-by-step explanation:

Solving for y, we can find the slope of the given line. It is the coefficient of x, 1/6.

  -12y = -2x -1

  y = 1/6x +1/12

The perpendicular line will have a slope that is the negative reciprocal of this:

  m = -1/(1/6) = -6

The y-intercept will be the y-value corresponding to x=0. That value is b=9, given to us by the point the line is to go through. So, we have the slope-intercept form ...

  y = mx + b

  y = -6x + 9

Answer:

see below

Step-by-step explanation:

z = 9 + 3i

This is in the form a+bi   where a is the real part and b is the imaginary part

1.The real part is 9

2. The imaginary part is 3

The complex conjugate is a-bi

3. complex conjugate 9-3i

4. 3i - z = 3i - (9+3i) = 3i -9 - 3i = -9

5. z-9 = 9+3i - 9 = 3i

6.  9-z = 9- (9+3i) = 9-9-3i = -3i

Answer:

16

Step-by-step explanation:

Using pythagorean theorem, a^2+b^2=c^2, you can substitute the legs in. 8^2+8sqrt3^2=c^2. C is the hypotenuse. you get 64+64sqrt9=c^2. This simplifies to 64+64(3)=c^2. This equals 256=c^2. Sqrt of 256 is 16, which is C.

Step-by-step explanation:

using a^2 = b^2+c^2

=> a^2 = 8^2 + 8×root3

=> a^2 = 64 + 64×3

=> a^2 = 64 + 192 = 256

=> a = 16

Answer:

  x = 6

Step-by-step explanation:

An angle bisector divides the segments on either side of it so they are proportional. That is ...

  x/12 = 5/10

  x = 12(5/10) = 6 . . . . . multiply by 12

Answer:

1st question: M=22.62 while C=75.38

2nd question: M=.22 while C=1.97

Step-by-step explanation:

If a mirror costing x dollars is marked up 30%, then we have to find x such that 30%x+x is 98 dollars.

We are solving:

.3x+x=98

Combine like terms:

1.3x=98

Divide both sides by 1.3:

x=75.38

M=98-75.38=22.62

C=75.38

So M=22.62 while C=75.38.

If ream of paper cost x and is marked up 11%, then we have to find x such that 11%x+x is 2.19.

We are solving:

.11x+x=2.19

1.11x=2.19

x=1 97

M=2.19-1.97=.22

So M=.22 while C=1.97

Answer:

A mirror selling for $98, marked up 30%;

M = $22.62

C = $75.38

A ream of paper selling for $2.19, marked up 11%;

M = $0.22

C = $1.97

Step-by-step explanation:

Hope it helps.

Answer: False

Step-by-step explanation: I believe it would be false. Using the law of sines with the side lengths of 113.29 feet and 125 feet, and the corresponding angels of 25 and 65 degrees, the angle of the light is about 58.29. I believe this would make it false as the angle is incorrect.

Answer:

  a) 0.2562

  b) no

Step-by-step explanation:

a) A binomial probability calculator or app can tell you that for bin(941, 0.75) the probability P(X ≥ 715) ≈ 0.2562

__

b) "significantly high" usually means the probability is less than 5%, often less than 1%. An event that occurs when its probability is almost 26% is not that unusual.

-- average price of gas ... continuous.  An average can come out to be any number, with a huge string of decimal places.  There are no numbers it CAN'T be.

-- car's speed ... continuous.  Between zero and the car's maximum top speed, there are no numbers it CAN'T be.

-- number of cars ... discrete.  It has to be a whole number.  There can't be a half a car or 0.746 of a car passing through.  

-- number of phone calls ... discrete.  It has to be a whole number.  There can't be a half of a call or 0.318 of a call made.

-- salaries ... I'm a little fuzzy on this one.  The employer can set a person's salary to be anything he wants it to be.  If they want it to be a whole number, or ANY fraction, they can do it ... there's no number it CAN'T be.  BUT ... when it comes time to actually pay him, THAT has to be a whole number of pennies.  There are actually a lot of numbers that they CAN'T pay, because they can't give him half of a penny, or 0.617 of a penny.

So I'm going to say that salary is a discrete variable.  

Answer:

95% confidence interval for the population mean is 20.255 and 17.945

Step-by-step explanation:

given data

mean = 19.1

standard deviation = 1.5

n = 9

to find out

95% confidence interval for the population mean

solution

we know 95% confidence interval formula i.e.

mean +/- t * standard deviation/[tex]\sqrt{n}[/tex]   .............1

here t for 9 students 2.31 ( from t table)

so put all value n t standard deviation and mean in equation 1

= mean +/- t * standard deviation/[tex]\sqrt{n}[/tex]

= 19.1 +/- 2.31 * 1.5/[tex]\sqrt{9}[/tex]

= 19.1 +/- 2.31 * 1.5/[tex]\sqrt{9}[/tex]  

= 20.255 and 17.945

95% confidence interval for the population mean is 20.255 and 17.945

The 95% confidence interval for the population mean of student ages, based on a sample mean of 19.1, standard deviation of 1.5, and a sample size of 9, is approximately (17.95, 20.25).

To construct a 95% confidence interval for the sample mean, first you need to know the sample mean, the sample standard deviation, and the sample size. In this case, the pertinent information is as follows: the sample mean (X) is 19.1 years, the sample standard deviation (s) = 1.5 years, and the sample size (n) = 9. The formula used for a 95% confidence interval is X ± t*(s/√n). In this case, the value for 't' with 8 degrees of freedom (n-1) is approximately 2.306 from the t-distribution table.

To calculate the 95% confidence interval, we then substitute the known values into the formula: 19.1 ± 2.306*(1.5/√9), yielding an interval of 19.1 ± 1.15, so the 95% confidence interval for the population mean is approximately (17.95, 20.25). This means that we estimate with 95% confidence that the true average age of all students in the class is between 17.95 and 20.25 years.

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Let Home runs = X

Triples would be X-3 ( 3 less triples than home runs)

Doubles would be 3x ( 3 times as many doubles as home runs)

Singles would be 45(x-3) ( 45 times as many singles as triples)

Simplify the equation for singles to be 45x-153

Now you have X + x-3 + 3x + 4x-135 = 262

Simplify:

50x - 138 = 262

Add 138 to both sides:

50x = 400

Divide both sides by 50:

x = 400/50

x = 8

Home runs = x = 8

Triples = x-3 = 8-3 = 5

Doubles = 3x = 3(8) = 24

Singles = 45(x-3) = 45(8-3) = 45(5) = 225

By setting up a system of equations using the given relationships between the types of hits, we can calculate that Ichiro Suzuki hit 225 singles, 24 doubles, 5 triples, and 8 home runs in the 2004 season.

To solve this problem, we will set up a system of equations based on the information given:

The total number of hits is the sum of singles, doubles, triples, and home runs, which gives us the equation:

S + D + T + H = 262

Substitute the expressions for T, D, and S in terms of H into this equation:

45(H - 3) + 3H + (H - 3) + H = 262

This simplifies to:

45H - 135 + 3H + H - 3 + H = 262

Combining like terms yields:

50H - 138 = 262

Add 138 to both sides to get:

50H = 400

Divide by 50 to find H:

H= 8

Using H, we can find T, D, and S:

Therefore, Ichiro Suzuki hit 225 singles, 24 doubles, 5 triples, and 8 home runs in the 2004 season.

Answer:

Option B  7sqrt2

Step-by-step explanation:

I assume that in the right triangle y and 7 are the legs and x is the hypotenuse

so

we know that

In the right triangle

cos(45)=7/x ----> the cosine of angle of 45 degrees is equal to divide the adjacent side to angle of 45 degrees by the hypotenuse

In this problem y=7 because is a 45-90-45 triangle

Remember that

cos(45)=√2/2

equate the equations

√2/2=7/x

x=14/√2

x=14/√2*(√2/√2)=14√2/2=7√2 units

Answer:

10 in

Step-by-step explanation:

So we want to consider the surface area of this sphere.

The formula for surface area of a sphere is [tex]A=4 \pi r^2[/tex].

So we have that the surface area is [tex]100 \pi[/tex].

So I'm going to replace [tex]A[/tex] in [tex]A=4 \pi r^2[/tex] with  [tex]100 \pi[/tex].

[tex]100\pi=4\pi r^2[/tex]

Now our main objective here is to solve for [tex]r[/tex]:

Divide both sides by [tex]4 \pi[/tex]:

[tex]\frac{100\pi}{4 \pi}=\frac{4\pi r^2}{4 \pi}[/tex]

This gets us [tex]r^2[/tex] by itself:

[tex]25=r^2[/tex]

What number squared gives you 25? If you don't know, just take the square root of both sides giving you:

[tex]\sqrt{25}=r[/tex]

Now you can just put [tex]\sqrt{25}[/tex] in your calculator.  You should get 5.

5 is the radius

The diameter is twice the radius.

So 2(5) is 10, so the diameter is 10 in.

Answer:

C) 10.0 in.

Step-by-step explanation:

If Hasan is painting a spherical model of a human cell for his science class and uses 100π square inches of paint (in one coat) to evenly cover the outside of the cell, the diameter of Hasan’s cell model is 10.0 inches.

Radius = 5

Diameter = Radius x 2

Therefore 5 x 2 = 10

The diameter is 10 in.

The answer of this question is c) 14

MN=NO

4x-5=2x+1

2x=6

x=3

Again

MO=MN+NO

MO=4×3-5+2×3+1

MO=7+7

MO=14

Answer:

First we need to calculate the height of the triangle ( because from that, we can also calculate both x and y)

We know that: h² = b'c'

And in our case:

b' = 9

c' = 3

=> h² = b'c' = 9 · 3

=> h = √(9 · 3) = √27

Now using pythagorean theorem:

(√27)² + 3² = x²

=> x²           = 27 + 9

=> x             = √(27 + 9) = √36 = 6

So x = 6 and the answer is C.

In a triangle, you can define proportions by setting the length ratios and width ratios equal to each other. For example, if you have a triangle with side lengths of 10, 8, and 6 inches, you can set up the proportion 10/8 = 8/6.

In a triangle, there are two common types of proportions: the length ratios and the width ratios.

To define these proportions, you can set the two length ratios equal to each other and the two width ratios equal to each other.

For example, let's say you have a triangle with side lengths of 10 inches, 8 inches, and 6 inches. You can set up the proportion:

10/8 = 8/6

Similarly, for the width ratios, you can set up the proportion:

w/30 = 0.5/5

Answer:

  (4, -2)

Step-by-step explanation:

The point-slope form of the equation for a line is ...

  y -k = m(x -h)

for a line with slope m through point (h, k).

Comparing this to the equation you're given, you can see that the point that was used is (h, k) = (4, -2).

_____

You can find other points on the line, but this one is the easiest to find, since it can be read directly from the equation.

Jamie's elevation during a hike is modeled with a piece-wise function depicting a constant rate of ascent and descent at 300 feet/hour up to a peak at 1,500 feet. He reaches 600 feet elevation at 2 and 8 hours, during his ascent and descent, respectively.

The subject of this question is Jamie's hiking adventure up and down a mountain, modeled by a mathematical equation. Since Jamie is hiking at a constant rate of 300 feet per hour, he reaches the peak of 1,500 feet in 5 hours (1,500 / 300). His elevation, e, can be calculated as e = 300t for t <= 5 because this represents his ascent. For the descent, the equation would be e = 1500 - 300(t - 5) for t > 5. This is because for every hour after the 5th hour, he will be descending at the same constant rate.

Therefore, if we were trying to calculate when his elevation would be 600 feet, there would be two possible answers: one during his ascent, and the other during his descent. For the ascent, we would solve 300t = 600, resulting in t = 2 hours. For the descent, we would solve 1500 - 300(t - 5) = 600, giving us t = 8 hours. So, Jamie is at 600 feet elevation both 2 hours into his hike (on his way up) and 8 hours into his hike (on his way down).

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The question involves creating a mathematical model for a hiking scenario, considering time and distance. Jamie hikes at a rate of 300 feet/hour for 5 hours up and 5 hours down, making a piecewise function the best way to model his elevation at any part of his journey.

The subject of the question is about understanding how to create a mathematical model for a hiking scenario. A key point is understanding that the rate of climbing and descending is the same and that time and distance are both relevant in this case.

Jamie climbs upwards at 300 feet/hour, making it to 1,500 feet, which means it took him (1,500 feet / 300 feet per hour) = 5 hours. After reaching the peak, he descends at the same rate. So his total journey time is 5 hours upwards + 5 hours downwards = 10 hours.

To model Jamie's elevation at any given time, we'd use a piecewise function because his elevation changes direction at the peak of the mountain. When t ≤ 5, we can define his elevation as e = 300t. After reaching the peak, his elevation drops at the same rate: when t > 5, e = 3000 - 300t. This gives us his elevation at any time during his hike.

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Answer:

Part 1) [tex]-1.25[/tex] -------> [tex]2.75/(-2.2)[/tex]

Part 2) [tex]-4\frac{1}{3}[/tex] --------> [tex](-2\frac{3}{5}) / (\frac{3}{5})[/tex]

Part 3) [tex]\frac{2}{3}[/tex] ------> [tex](-\frac{10}{17}) / (-\frac{15}{17})[/tex]

Part 4) [tex]3[/tex] ------> [tex](2\frac{1}{4}) / (\frac{3}{4})[/tex]

Step-by-step explanation:

Part 1) we have

[tex]2.75/(-2.2)[/tex]

To calculate the division problem convert the decimal number to fraction number

[tex]2.75=275/100\\ -2.2=-22/10[/tex]      

so

[tex](275/100)/(-22/10)[/tex]

Remember that

Since division is the opposite of multiplication, you can turn this division problem into a multiplication problem by multiplying the top fraction by the reciprocal of the bottom fraction

[tex](275/100)/(-22/10)=(275/100)*(-10/22)=-(275*10)/(22*100)=-(275)/(220)[/tex]

Simplify

Divide by 22 both numerator and denominator

[tex]-(275)/(220)=-125/100=-1.25[/tex]

Part 2) we have

[tex](-2\frac{3}{5}) / (\frac{3}{5})[/tex]

To calculate the division problem convert the mixed number to an improper fraction  

[tex](-2\frac{3}{5})=-\frac{2*5+3}{5}=-\frac{13}{5}[/tex]

so

[tex](-\frac{13}{5}) / (\frac{3}{5})[/tex]

Since division is the opposite of multiplication, you can turn this division problem into a multiplication problem by multiplying the top fraction by the reciprocal of the bottom fraction

[tex](-\frac{13}{5}) / (\frac{3}{5})=(-\frac{13}{5})*(\frac{5}{3})=-\frac{13*5}{5*3}=-\frac{13}{3}[/tex]

Convert to mixed number

[tex]-\frac{13}{3}=-(\frac{12}{3}+\frac{1}{3})=-4\frac{1}{3}[/tex]

Part 3) we have

[tex](-\frac{10}{17}) / (-\frac{15}{17})[/tex]

Since division is the opposite of multiplication, you can turn this division problem into a multiplication problem by multiplying the top fraction by the reciprocal of the bottom fraction

[tex](-\frac{10}{17}) / (-\frac{15}{17})=(-\frac{10}{17})*(-\frac{17}{15})=\frac{10*17}{17*15}=\frac{10}{15}[/tex]

Simplify

Divide by 5 both numerator and denominator

[tex]\frac{10}{15}=\frac{2}{3}[/tex]

Part 4) we have

[tex](2\frac{1}{4}) / (\frac{3}{4})[/tex]

To calculate the division problem convert the mixed number to an improper fraction  

[tex](2\frac{1}{4})=\frac{2*4+1}{4}=\frac{9}{4}[/tex]

so

[tex](\frac{9}{4}) / (\frac{3}{4})[/tex]

Since division is the opposite of multiplication, you can turn this division problem into a multiplication problem by multiplying the top fraction by the reciprocal of the bottom fraction

[tex](\frac{9}{4}) / (\frac{3}{4})=(\frac{9}{4})*(\frac{4}{3})=\frac{9*4}{4*3}=\frac{9}{3}=3[/tex]

To match each division problem to its quotient, you'll need to perform each division and then see which of the given quotients corresponds to the result of each division. Let's go through the steps for each division problem you might have:
1. Start with the first division problem. For example, if it's `45 / 5`, you'd perform the division by determining how many times 5 goes into 45.
2. To solve `45 / 5`, you can count by fives until you reach 45, or recognize that 5 times 9 is 45. Hence, the quotient for `45 / 5` is 9.
3. Look at the potential quotients given to you and match the result. If one of the choices is 9, match `45 / 5` with that quotient.
4. Repeat the process for the next division problem, say `30 / 6`. Divide 30 by 6 to get the quotient. Since 6 times 5 is 30, the quotient here is 5.
5. Again, look at your potential quotients. If there is a 5 among them, this is incorrect since 5 is not a choice in our example set of potential quotients. Instead, you would expect to see a 6, as that is the typical mistake that such a setup might be aiming to identify.
6. Move on to the next division problem, for instance, `18 / 3`. To find the quotient, you divide 18 by 3, which gives you 6 because 3 times 6 is 18.
7. Match `18 / 3` with the correct quotient from your list of choices, which in this case would be 6.
Remember, these are hypothetical examples. In your actual matching exercise, you would perform the division for each problem you've been given and then find the corresponding quotient from the choices available to you. The key is to perform each division accurately and then pair it with the right answer. If you perform all the divisions and none of the quotients match the results you have obtained, there might be an error in the given quotients or the division problems.

Answer:

y = 4.8

Step-by-step explanation:

Since AM is an angle bisector then the following ratios are equal

[tex]\frac{AC}{AB}[/tex] = [tex]\frac{CM}{MB}[/tex], that is

[tex]\frac{9.6}{8}[/tex] = [tex]\frac{y}{4}[/tex] ( cross-  multiply )

8y = 38.4 ( divide both sides by 8 )

y = 4.8

Answer: 70% chance of winning

Step-by-step explanation: What is your question? Are you trying to ask the probability of winning? (I will assume this and answer)

The whole case of selecting to numbers : 5C2 = 5 X 4 / 2 = 10

the cases of getting a odd sum : select 1 odd number and 1 even number

=> select 1 odd number : 7 or 9 => 2 cases

=> select 1 even number: 4,6,8 => 3 cases

you multiply 2 and 3 and divide it by 2 because order doesn't matter

so the answer is 1 - (3/10) = 0.7  

The player in the game has an equal chance of winning or losing.

In this problem, we are given a box containing five slips of paper, each with a number written on it. The first player draws two slips and adds the two numbers together. To determine if the player wins or loses, we need to determine if the sum of the two numbers is even or odd.

To solve this problem, we can list all the possible pairs of numbers and find out if the sum of each pair is even or odd. If the sum is even, the player wins; if the sum is odd, the player loses. We can do this by considering the possible outcomes:

From the listed outcomes, we can see that there are 5 even sums and 5 odd sums.

Therefore, the player has an equal chance of winning or losing in this game.

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Answer:

i think its C

Step-by-step explanation:

the frequency is in median form and the speed is in mean form

Answer:

Step-by-step explanation:

There are 40 numbers in your data set. (This is the sum of the numbers in the Frequency column.) This is an even number, so the median is the average of the middle two Speed values when they are sorted from lowest to highest. The frequency chart already tells you the result of that sorting. From the chart, we can see that there are 9 Speed values below 15, and 12 values that are 15. That tells us that Speed values number 20 and 21 on the list both have a value of 15, so that is the value of the median.

__

The mode is the value that occurs most frequently. Obviously that value is 15, since it occurs 12 times and no other number occurs more than 6 times.

__

Finding the mean is a little more work. For that, we have to add up the 40 numbers and divide by 40. The fact that some numbers are repeated can help shorten that effort.

  sum of all values = 12×1 + 13×2 + 14×6 + 15×12 + 16×6 + 17×5 + 18×1 + 19×2 + 20×4 + 21×1 = 640

  mean = (sum of all values)/(number of values) = 640/40

  mean = 16

[tex]|\Omega|=3\cdot3=9\\|A|=1\cdot2=2\\\\P(A)=\dfrac{2}{9}\approx22\%[/tex]

Answer:

(B) sample size is 666

Step-by-step explanation:

given data

CI = 99%

error = 0.05

to find out

sample size

solution

we know that for CI = 99% and E = 0.05 the value of z = 2.58 from table

and no estimate of proportion is given so it is rule take q = p = 0.5

so now we can calculate sample size i.e.

n = (z/E)² ×p ×q

put the value q and p = 0.5 and z and E so we get sample size

n = (z/E)² ×p ×q

n = (2.58/0.05)² ×0.5 ×0.5

n = 665.64

so sample size is 666

so option (B) is right

A) 177.568 thousand.

B) 125.836 thousand.

In this question, it is asking you to use the equation to find the population of ladybugs in a certain year.

Equation we're going to use:

[tex]y = -1.437 x + 197.686[/tex]

We know that the "x" variable represents the number of years since 2010, so that means our starting year is 2010.

Lets solve the question.

Question A:

We need to find the ladybug population is 2024.

2024 is 14 years after 2010, so our "x" variable will be replaced with 14.

Your equation should look like this:

[tex]y = -1.437 (14) + 197.686[/tex]

Now, we solve.

[tex]y = -1.437 (14) + 197.686\\\\\text{Multiply -1.437 and 14}\\\\y=-20.118+197.686\\\\\text{Add}\\\\y=177.568[/tex]

You should get 177.568

This means that the population of ladybugs in 2024 is 177.568 thousand.

Question B:

We need to find the ladybug population is 2060.

2060 is 50 years after 2010, so the "x" variable would be replaced with 50.

Your equation should look like this:

[tex]y = -1.437 (50) + 197.686[/tex]

Now, we solve.

[tex]y = -1.437 (50) + 197.686\\\\\text{Multiply -1.437 and 50}\\\\y=-71.85+197.686\\\\\text{Add}\\\\y=125.836[/tex]

This means that the population of ladybugs in 2060 would be 125.836 thousand.

Answer:

$520

Step-by-step explanation:

Since this is a 5% discount, you must subtract 5 from 100% which is 95%.

This will be written as 0.95.

Expression: [tex]x*0.95=494\\\\0.95x=494\\\\\frac{0.95x}{0.95} =\frac{494}{0.95}[/tex]

The answer will be $520.

Answer:

[tex]\boxed{520}[/tex]

Step-by-step explanation:

[tex]\begin{array}{rcl}\text{ Price before discount - discount} & = & \text{sale price}\\b-0.05b & = & 494\\0.95b & = & 494\\\\b & = & \dfrac{494 }{0.95}\\\\& = & \mathbf{520}\\\end{array}\\\text{The number from the set that matches } b \text{ is }\boxed{\mathbf{520}}[/tex]

Answer:

3000 g & 4000 g

Step-by-step explanation:

Edge 2021

According to the empirical rule, 68% of all newborn babies in the United States weigh between 3000 g and 4000 g.

According to the empirical rule, also known as 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95% and 99.7% of the values lies within one, two or three standard deviations of the mean of the distribution.

[tex]P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(\mu - 2\sigma < X < \mu + 2\sigma) = 95\%\\P(\mu - 3\sigma < X < \mu + 3\sigma) = 99.7\%[/tex]

Here, mean of distribution of X is [tex]\mu[/tex]  and standard deviation from mean of distribution of X is [tex]\sigma[/tex]

In the United States, birth weights of newborn babies are approximately normally distributed with a mean of

[tex]\mu = 3,500\rm \;g[/tex]

The standard deviation of the babies is,

[tex]\sigma = 500 g[/tex]

Put the value in the empirical formula for 68% as,

[tex]P(3500-500 < X < 3500+ 500) = 68\%\\P(3000 < X < 4000) = 68\%[/tex]

Hence, according to the empirical rule, 68% of all newborn babies in the United States weigh between 3000 g and 4000 g.

Learn more about empirical rule here:

https://brainly.com/question/13676793

Answer:

-sqrt(5) ≤ x ≤ sqrt(5)

Step-by-step explanation:

x^2-5≤0

Add 5 to each side

x^2-5+5≤0+5

x^2 ≤5

Take the square root of each side, remembering to flip the inequality for the negative sign.  Since this is less than we use and in between

sqrt(x^2) ≤ sqrt(5)   and sqrt(x^2) ≥ -sqrt(5)  

x ≤ sqrt(5) and x ≥- sqrt(5)  

-sqrt(5) ≤ x ≤ sqrt(5)