Bert and Ernie are missing each other and their friend Big Bird They want to meet at Big Bird's nest which is halfway from their apartments. The distance from Bert's apartment to Big Bird's nest (5x + 4) ismiles away while Ernie's apartment to Big Bird's nest is (15x-30) miles away How far are Bert and Ernie's apartments from Big Bird's nest?

Answer:

A, C, E

Step-by-step explanation:

From the table you can see that the water depth cahnges

[tex]0.8-0.4=1.2-0.8=1.6-1.2=2.0-1.6=0.4\ in[/tex]

for every

[tex]4-2=6-4=8-6=10-8=2\ in[/tex] of snow (option B is false).

This means that the function modelling this situation is linear function (option A is true and option D is false). Let the equation of this function be [tex]y=ax+b.[/tex] Then

[tex]0.4=2a+b,\\ \\0.8=4a+b.[/tex]

Subtract these two equations:

[tex]2a=0.8-0.4,\\ \\2a=0.4,\\ \\a=0.2.[/tex]

Hence,

[tex]b=0.4-2\cdot 0.2=0.[/tex]

The equation of the straight line (the graph of linear function) is [tex]y=0.2x.[/tex] (option E is true) This line passes through the point (0,0), because its coordinates satisfy the equation (option C is true).

Answer:

A and C

Step-by-step explanation:

Ok listen here. The guy from the other thing said ACE however thats so wrong that I can't explain how wrong that is. how is it wrong you might ask. Well if you can READ the question you know that you should select 2 options

second of all f(x)=0.2^x is saying that if x equals 2 then y is 0.2*0.2 which is 0.04 which is not the result.

I hope this helps more than whatever answer the other answer was. If not then you gotta figure it out yourself

Answer:

16 minutes

Step-by-step explanation:

Answer:

Beatrice is incorrect. All of these points are not on the same line because the slope between (-2, -1) and (1, 0), which are coordinates from each of the pairs above, is not equivalent equal to 1/2

Step-by-step explanation:

The answer is: incorrect; are not; is not. Beatrice is incorrect. All of these points are not on the same line because the slopes between (-2,-1) and (1,0)  is not equal to [tex]\frac{1}{2}[/tex].

Beatrice is incorrect. All of these points are not on the same line because the slope between (-2,-1) and (1,0) is not equal to 1/2.

Here’s a step-by-step explanation:

   [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex].

Since the slopes between these points vary, they do not lie on the same line. All three sets must have the same slope to be considered collinear.

Answer:

The correct answer option is 4/11

Step-by-step explanation:

We know that the word 'probability' has 11 alphabets.

We are to find to find the probability of getting a 'b' or an 'i' from this word.

Probability of getting a b = [tex]\frac{2}{11}[/tex] (since there are 2 b's in probability)

Probability of getting an i = [tex]\frac{2}{11}[/tex] (since there are 2 i's in probability)

Probability of getting 'b' or 'i' = [tex]\frac{2}{11} + \frac{2}{11} = \frac{4}{11}[/tex]

Answer:

5.25 or 5 1/4 MPH

Step-by-step explanation:

1. convert 15 3/4 into a decimal = 15.75

2. divide the miles canoed (15.75) by the time (3)

    15.75/3 = 5.25 MPH

The probability of picking a green jelly bean with the first pick is 4/14 = 2/7, because there are 14 jelly bean in total (6 red + 4 green + 4 blue) and 4 of them are green.

If you pick a green jelly bean at the beginning, you have 13 jelly beans remaining, of which 6 are red. So, the probability of picking a red jelly bean is now 6/13.

You want these two events to happen one after the other, to be more precise you want to pick a green jelly bean with the first pick AND a red jelly bean with the second pick. We know the probabilities of the two events, so we have to multiply them to get the probability of them happening both:

[tex]\dfrac{2}{7}\cdot\dfrac{6}{13}=\dfrac{12}{91}[/tex]

Answer:

I need numbers to actually calculate the problem.

Step-by-step explanation:

Answer:36ft^3

Step-by-step explanation:

Answer:

  c.  (π/2 -1) square units

Step-by-step explanation:

A segment that subtends an arc of θ in a circle of radius r has an area given by ...

  A = (1/2)(θ -sin(θ))r² . . . . . where θ is in radians

In your figure, the radius is r = √2 and the angle is 90°, so θ = π/2. Then the area is ...

  A = (1/2)(π/2 -sin(π/2))·(√2 units)²

  A = (π/2 -1) units²

Answer:

y = -x-3

x-y = -3

x - 2y = 10

Step-by-step explanation:

x − 3y = 6

Slope intercept form is y = mx +b

We need to solve for y

Subtract x from each side

x-x-3y = -x+6

-3y = -x +6

Divide each side by -3

-3y/-3 = -x/-3 +6/-3

y = 1/3 x -2

Standard form is Ax +By = C

y = -x-3

Add x to each side

x-y = -x+x-3

x-y = -3

y = 1/2x -5

We do not like fractions in standard form, so multiply by 2

2y = 2*1/2x -2*5

2y =x-10

Subtract x from each side

-x +2y = x-x-10

-x+2y = -10

We like to have the coefficient on x be positive

Multiply by -1

x - 2y = 10

Answer:

[tex]\begin{array}{ccccc}\text{January}&\text{February}&\text{March}&\text{April}&\text{May}\\\dfrac{3}{20}&\dfrac{5}{20}&\dfrac{2}{20}&\dfrac{8}{20}&\dfrac{2}{20}\end{array}[/tex]

Step-by-step explanation:

During 5 months Laura wrote

3+5+2+8+2=20 songs.

1. The probability that the song was written in January is [tex]\frac{3}{20}.[/tex]

2. The probability that the song was written in February is [tex]\frac{5}{20}.[/tex]

3. The probability that the song was written in March is [tex]\frac{2}{20}.[/tex]

4. The probability that the song was written in April is [tex]\frac{8}{20}.[/tex]

5. 1. The probability that the song was written in May is [tex]\frac{2}{20}.[/tex]

The probabolity distribution table:

[tex]\begin{array}{ccccc}\text{January}&\text{February}&\text{March}&\text{April}&\text{May}\\\dfrac{3}{20}&\dfrac{5}{20}&\dfrac{2}{20}&\dfrac{8}{20}&\dfrac{2}{20}\end{array}[/tex]

Answer:

-35

Step-by-step explanation:

[tex]5p/7-18=-43[/tex] ⇒ [tex]5p/7=-43+18[/tex] ⇒

[tex]7(5p/7=- 25)7[/tex] ⇒ [tex]5p=-175[/tex] ⇒

[tex]5p/5 = -175/5[/tex] ⇒ [tex]p = -35[/tex]

There's literally unlimited answers but here are some simple ones.

5 x 11 = 55

55 = 55

55 > 54

1 < 55

3 x 2 < 55

To compare numbers to 55, choose numbers less than, greater than, or equal to 55 and use the appropriate comparison operator. Examples include 50 < 55 (less than), 55 = 55 (equal to), and 60 > 55 (greater than).

To compare numbers with 55 using the comparison operators >, <, and =, we must choose numbers that are either greater than, less than, or equal to 55. For example:

When you are comparing numbers, always remember that a number is greater than another if it represents a larger quantity, and it is less than another if it represents a smaller quantity. The equal sign is used when the quantities are identical.

Answer:

A:

Step-by-step explanation:

***I'm pretty sure A should read "NO, because the test value 1.257 is less than the critical value 1.782.  Please check the wording of the problem***

H0 : μ ≤ 400

Ha : μ > 400 (claim)

Sample mean: 6,155/13

Sample standard deviation: √44422.4359

Critical test value:   t > 1.782

t =  (6,155/13 - 400)/[(√44422.4359)/√13]   =   1.257    

    1.257 < 1.782  ;  we fail to reject the null hypothesis

There is not enough evidence at the 5% level of significance to support the claim that the mean  battery life is at least 400 hours.  

The correct Answer is: x= -5

It's me again ok so

Simplifying

5x = -25

Solving

5x = -25

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Divide each side by '5'.

x = -5

Simplifying

x = -5

BOOM

Answer:

0.40

Step-by-step explanation:

Members who run only  long distance = 8%

So, probability that a member will run only long distance = P(A) = 0.08

Members who compete only in field events = 32%

So, probability that a member will compete only in field events = P(B) 0.32

Members who are sprinters = 12%

So, probability that a member is sprinter = P(C) 0.12

We have to calculate the probability that a randomly chosen team member runs only long-distance or competes only in field events. i.e we have to find P(A or B). Since these events cannot occur at the same time, we can write:

P(A or B) = P(A) + P(B)

Using the values, we get:

P(A or B) = 0.08 + 0.32 = 0.40

Thus, the probability that a randomly chosen team member runs only long-distance or competes only in field events is 0.40

The probability that a randomly chosen team member runs only long-distance or competes only in field events is 0.40.

1. To find the probability that a randomly chosen team member runs only long-distance or competes only in field events, we need to add the probabilities of these two mutually exclusive events.

2. Given:

3. Since these events are mutually exclusive (they cannot happen at the same time), we simply add the probabilities:

P(long-distance or field events) = P(long-distance) + P(field events)

P(long-distance or field events) = 0.08 + 0.32 = 0.40

Therefore, the probability that a randomly chosen team member runs only long-distance or competes only in field events is 40% or 0.40.

Answer:

[tex]\large\boxed{e.\ \{a,\ b,\ c,\ d,\ 0,\ 2\}}[/tex]

Step-by-step explanation:

[tex]\text{The union (denoted by}\ \cup\ \text{) of a collection of sets is the set of all elements of the sets. }\\\\A=\{0,\ 1,\ 2,\ 3\}\\\\B=\{a,\ b,\ c,\ d\}\\\\C=\{0,\ a,\ 2,\ b\}\\\\B\ \cup\ C=\{a,\ b,\ c,\ d,\ 0,\ 2\}[/tex]

1,8272 --- 8,000

17,282 --- 80

8,000÷80=100 times greater

Final answer:

The value of 8 in the number 18,272 (8,000) is 100 times greater than its value in the number 17,282 (80).

Explanation:

The question is asking how many times the value of 8 in 18,272 is greater than the value of 8 in 17,282.

In the number 18,272, the 8 is in the thousands place, making it have a value of 8,000. In the number 17,282, the 8 is in the tens place, giving it a value of 80.

To determine how many times greater the value of 8 is in the first number compared to the second, divide the larger value by the smaller value: 8,000 ÷ 80 = 100.

Therefore, the value of 8 in 18,272 is 100 times greater than in 17,282.

Answer:

The distance between the boats is [tex]50\ mi[/tex]

Step-by-step explanation:

we know that

The Pythagoras Theorem states that

In a right triangle

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

where

c is the hypotenuse

a and b are the legs

In this problem

Let

c  ----> the distance between the boats

a -----> the horizontal distance between the boats

b -----> the vertical distance between the boats

[tex]a=12+18=30\ mi[/tex]

[tex]b=16+24=40\ mi[/tex]

substitute the values

[tex]c^{2}=30^{2}+40^{2}[/tex]

[tex]c^{2}=2,500[/tex]

[tex]c=50\ mi[/tex]

Final Answer:

The distance between the two boats is 50 miles.

Explanation:

To find the distance between the two boats after they have traveled, we need to determine the final position of each boat relative to the island, and then use the Pythagorean theorem to find the distance between these two positions. Let's go through the calculations step-by-step:

Step 1: Determine the final position of each boat relative to the island.
- Boat 1 travels 12 miles east and then 16 miles north. Let’s define east as the positive x-direction and north as the positive y-direction. So, the final coordinates of Boat 1 relative to the island are (12, 16).
- Boat 2 travels 24 miles south and then 18 miles west. Let’s define south as the negative y-direction and west as the negative x-direction. So, the final coordinates of Boat 2 relative to the island are (-18, -24).

Step 2: Determine the differences in the x and y coordinates between Boat 1 and Boat 2.
- The difference in x-coordinates dx is the x-coordinate of Boat 1 minus the x-coordinate of Boat 2:

[tex]\( dx = 12 - (-18) = 12 + 18 = 30 \)[/tex] miles.
- The difference in y-coordinates dy is the y-coordinate of Boat 1 minus the y-coordinate of Boat 2:

[tex]\( dy = 16 - (-24) = 16 + 24 = 40 \)[/tex] miles.

Step 3: Use the Pythagorean theorem to calculate the distance between the two boats.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse c (the side opposite the right angle) is equal to the sum of the squares of the other two sides a and b:
[tex]\[ c^2 = a^2 + b^2 \][/tex]

Here, dx and dy can be considered the lengths of the sides of a right triangle, and the distance between the boats d is the hypotenuse of this triangle. So:
[tex]\[ d = \sqrt{dx^2 + dy^2} \\\\\[ d = \sqrt{30^2 + 40^2} \\\\\[ d = \sqrt{900 + 1600} \\\\\[ d = \sqrt{2500} \\\\\[ d = 50 \][/tex]

Therefore, the distance between the two boats is 50 miles.

9514 1404 393

Answer:

  157 seconds

Step-by-step explanation:

The volume of the pail is ...

  V = πr^2·h

  V = 3.14(5 in)^2(16 in) = 1256 in^3

At 8 in^3/s it will take ...

  (1256 in^3)/(8 in^/s) = 157 s

to fill the pail.

It will take 157 seconds to fill the pail with milk.

Answer:

C. 2916

Step-by-step explanation:

The given limits is

[tex]\lim_{h \to 0} \frac{f(9+h)-f(9)}{h}[/tex]

if [tex]f(x)=x^4[/tex].

[tex]\Rightarrow f(9)=9^4=6561[/tex]

[tex]f(h+9)=(h+9)^4=h^4+36 h^3+486 h^2+2916 h+6561[/tex]

Our limit becomes;

[tex]\lim_{h \to 0} \frac{f(h+9)-f(9)}{h}= \lim_{h \to 0} \frac{h^4+36 h^3+486 h^2+2916 h+6561-6561}{h}[/tex]

This simplifies to;

[tex]\lim_{h \to 0} \frac{f(h+9)-f(9)}{h}= \lim_{h \to 0} \frac{h^4+36 h^3+486 h^2+2916 h}{h}[/tex]

[tex]\lim_{h \to 0} \frac{f(h+9)-f(9)}{h}= \lim_{h \to 0} h^3+36 h^2+486 h+2916 [/tex]

[tex]\lim_{h \to 0} \frac{f(h+9)-f(9)}{h}= (0)^3+36 (0)^2+486(0)+2916 [/tex]

[tex]\lim_{h \to 0} \frac{f(h+9)-f(9)}{h}= 2916 [/tex]

the correct choice is C.

Answer:

$13.04 is the original price of the shirt

Step-by-step explanation:

As sales tax is 8% we will find the price of the shirt

11.34 * 8/100 = 0.91

11.34-0.91= 10.43

so, $10.43 is the price of the shirt after discount and excluding sales tax.

The original price of the shirt is:

10.43 * 25 /100 = 2.60

adding it to the price of shirt

10.43 + 2.61 = 13.04

Answer:

14 or 14.00

Step-by-step explanation:

If he is getting 25% off, that means that what he paid with 75% of the original cost. Don't forget that he also has to pay a percent tax so that is the same as multiplying by 1.08. (btw this is what it said the correct answer was after I get it wrong two times)

The sum of all the three interior angles of a triangle are 180 degrees. This does not depend on the positioning of the three sides. The sides can be positioned in any way, but the sum must be 180 degrees.

So, the best possible sets of measurements that could be the interior angle measures of a triangle are : 15°, 75°, 90°  And 60°, 60°, 60°

The sets of measurements that could represent the interior angles of a triangle are those whose angles add up to exactly 180°. The valid options provided are 10°, 10°, 160°; 15°, 75°, 90°; 35°, 35°, 105°; and the equilateral set of 60°, 60°, 60°.

The question pertains to the interior angles of a triangle. According to the Triangle Sum Theorem, the interior angles of a triangle always add up to 180°. Therefore, to determine which sets of measurements could represent the interior angles of a triangle, we must check if the sum of the given angles is equal to 180°.

From the options given, the sets of measurements that represent the interior angles of a triangle are:

Answer:

none of the above

Step-by-step explanation:

A graphing calculator shows the zeros to be x=-2, and a double zero at x=3. Hence the factorization is ...

(x +2)(x -3)^2 = 0

The premise that 4 is a zero is incorrect, and none of the answer choices include (x+2) as a factor. The problem is unworkable as written here.

Answer:

D  2x(3x+4) + 1(3x+4)

Step-by-step explanation:

(2x+1) (3x+4)

We need to FOIL

First 2x*3x = 6x^2

Outer 2x*4 = 8x

Inner 1*3x =3x

Last 1*4 =4

Add them together

6x^2 +8x+3x+4

Combine like terms

6x^2 +11x+4

This process is simply taking 2x (3x+4) and adding 1 (3x+4)

2x(3x+4) + 1(3x+4)

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

Explanation:

Triangle PQC is congruent to triangle RQC. We can prove this through use of the hypotenuse leg theorem (HL theorem). Note that PC = RC are congruent radii, and also note that CQ = CQ through the reflexive theorem. We have a pair of hypotenuses and a pair of legs for the right triangles.

Then through CPCTC (corresponding parts of congruent triangles are congruent), we know that the pieces PQ and QR are congruent. For now, let's just call them x. They must add to PR which is 12, so,

PQ + QR = PR ..... segment addition postulate

x + x = 12

2x = 12

x = 6 ..... divide both sides by 2

QR = 6

This shows that if you have a radius perpendicular to a chord of a circle, then the radius will bisect this chord. Bisect means to cut in half.

Step-by-step Answer:

There is a theorem in geometry that states that a perpendicular (CQ) to any chord (PR) bisects the chord.  This means that PQ=RQ=6cm.

QUESTION 1

The given logarithm is

[tex]8\log_g(x)+5\log_g(y)[/tex]

We apply the power rule of logarithms; [tex]n\log_a(m)=\log_(m^n)[/tex]

[tex]=\log_g(x^8)+\log_g(y^5)[/tex]

We now apply the product rule of logarithm;

[tex]\log_a(m)+\log_a(n)=\log_a(mn)[/tex]

[tex]=\log_g(x^8y^5)[/tex]

QUESTION 2

The given logarithm is

[tex]8\log_5(x)+\frac{3}{4}\log_5(y)-5\log_5(z)[/tex]

We apply the power rule of logarithm to get;

[tex]=\log_5(x^8)+\log_5(y^{\frac{3}{4}})-\log_5(z^5)[/tex]

We apply the product to obtain;

[tex]=\log_5(x^8\times y^{\frac{3}{4}})-\log_5(z^5)[/tex]

We apply the quotient rule; [tex]\log_a(m)-\log_a(n)=\log_a(\frac{m}{n} )[/tex]

[tex]=\log_5(\frac{x^8\times y^{\frac{3}{4}}}{z^5})[/tex]

[tex]=\log_5(\frac{x^8 \sqrt[4]{y^3} }{z^5})[/tex]

Answer:

The 3 geometric solids with circular cross sections are a sphere, a cone and a cylinder

Step-by-step explanation:

While a cone and a cylinder will not in every direction, if you slice them on a horizontal plane, they will have a circular cross section.

The sphere, cylinder, and cone are three-dimensional geometric solids with circular cross sections, existing in both solid and hollow forms, important in physics for understanding properties like moment of inertia and involvement in superelastic collisions.

Three geometric solids that possess circular cross sections are the sphere, cylinder, and cone. These shapes are known as three-dimensional solid figures. The sphere is a solid figure where all points on the surface are equidistant from the center, resulting in any cross-section through its center being a circle.

A cylinder is a solid with straight parallel sides and a circular or oval cross section. A cone has a flat circular base and tapers to a point called the apex or vertex, creating circular cross-sections when sliced parallel to the base.

In addition to fully solid forms, there are also hollow versions of these shapes, such as the hollow spherical shell, which still have circular cross sections. These solids can be involved in various physics concepts such as rotational dynamics and superelastic collisions. When analyzing the rotational motion or collision attributes of these solids, the shapes' geometrical and mass properties play a crucial role.

For instance, the moment of inertia of a solid sphere differs from that of a hollow spherical shell due to the distribution of mass within the object.

Answer:

1999

Step-by-step explanation:

y=-15x^2+64x+360

y=-15(1)^2+64(1)+360

y=409

(y is in millions)

I hope this helps!

Answer:

(-6, 1)

Step-by-step explanation:

We are given a point with the coordinates (-4, -2) and we are to plot this on a graph and then find another point by moving three units upwards and 2 units towards left.

If we move 3 units up from the point (-4, -2), we get (-4, 1).

Then from (-4, 1), we move 2 units towards left and we get the coordinates of this new point which are (-6, 1).

Answer:

Need to see the choices

Step-by-step explanation: