Can please someone help with this two problems?
Answer:
A and C
Step-by-step explanation:
20) Since the triangles are similar, you can say that 98 corresponds to 42 and 77 corresponds to 3x+6, because of this you can write an equation ((98/77)(3x-6) =42) and then simplify to get x = 13.
21) Since ABC and DFE are similar, we can say that 2x+2 corresponds to x+3 and 24 corresponds to 16. You can write this as the equation (24/2x+2)(x+3) = 16 and simplify to get x=5.
I hope this helps :)
Solve | 2x - 6 | = |x| by graphing
Answer:
X=2 & X=6
Step-by-step explanation:
If you graph the equation (I recommend using desmos) you can see that X equals 2 & 6.
A 10-foot ladder is leaning against a vertical wall. If the bottom of the ladder is being pulled away from the wall at the rate of 9 feet per second, at what rate is the area of the triangle formed by the wall, the ground, and the ladder changing, in square feet per second, at the instant the bottom of the ladder is 6 feet from the wall
Answer:
The area is changing at 15.75 square feet per second.
Step-by-step explanation:
The triangle between the wall, the ground, and the ladder has the following dimensions:
H: is the length of the ladder (hypotenuse) = 10 ft
B: is the distance between the wall and the ladder (base) = 6 ft
L: the length of the wall (height of the triangle) =?
dB/dt = is the variation of the base of the triangle = 9 ft/s
First, we need to find the other side of the triangle:
[tex]H^{2} = B^{2} + L^{2}[/tex]
[tex] L = \sqrt{H^{2} - B^{2}} = \sqrt{(10)^{2} - B^{2}} = \sqrt{100 - B^{2}} [/tex]
Now, the area (A) of the triangle is:
[tex] A = \frac{BL}{2} [/tex]
Hence, the rate of change of the area is given by:
[tex] \frac{dA}{dt} = \frac{1}{2}[L*\frac{dB}{dt} + B\frac{dL}{dt}] [/tex]
[tex] \frac{dA}{dt} = \frac{1}{2}[\sqrt{100 - B^{2}}*\frac{dB}{dt} + B\frac{d(\sqrt{100 - B^{2}})}{dt}] [/tex]
[tex]\frac{dA}{dt} = \frac{1}{2}[\sqrt{100 - B^{2}}*\frac{dB}{dt} - \frac{B^{2}}{(\sqrt{100 - B^{2}})}*\frac{dB}{dt}][/tex]
[tex]\frac{dA}{dt} = \frac{1}{2}[\sqrt{100 - 6^{2}}*9 - \frac{6^{2}}{\sqrt{100 - 6^{2}}}*9][/tex]
[tex]\frac{dA}{dt} = 15.75 ft^{2}/s[/tex]
Therefore, the area is changing at 15.75 square feet per second.
I hope it helps you!
The rate of change (ROC) of the area with respect to (w.r.t.) time can be
found from the ROC of the area w.r.t. x and the ROC of x w.r.t. time.
At the time the ladder is 6 feet from the wall, the area is increasing at 15.75 ft.²/sec.Reasons:
The length pf the ladder = 10 feet
Rate at which the ladder is pulled from the wall, [tex]\displaystyle \frac{dx}{dt}[/tex] = 9 feet per second
Required:
The rate at which the area of the triangle formed by the ladder, the wall
and the ground, is changing at the instant the ladder is 6 feet from the wall.
Solution:
The area the triangle, A = 0.5·x·y
Where;
x = The distance of the ladder from the wall
y = The height of the ladder on the wall
By Pythagoras's theorem, we have;
10² = x² + y²
Which gives;
y = √(10² - x²)
Therefore;
The area the triangle, A = 0.5 × x × √(10² - x²)
By chain rule, we have;
[tex]\displaystyle \frac{dA}{dt} = \mathbf{\frac{dA}{dx} \times \frac{dx}{dt}}[/tex]
[tex]\displaystyle \frac{dA}{dx} = \frac{d\left(0.5 \cdot x \cdot \sqrt{10^2 - x^2} }{dx} = \mathbf{\frac{\left(x^2 - 50\right) \cdot \sqrt{100-x^2} }{x^2-100}}[/tex]
[tex]\displaystyle \frac{dA}{dx} = \frac{\left(x^2 - 50\right) \cdot \sqrt{100-x^2} }{x^2-100}[/tex]
Therefore;
[tex]\displaystyle \frac{dA}{dt} = \mathbf{\frac{\left(x^2 - 50\right) \cdot \sqrt{100-x^2} }{x^2-100} \times 9}[/tex]
When the ladder is 6 feet from the wall, we have;
x = 6
[tex]\displaystyle \frac{dA}{dt} = \frac{\left(6^2 - 50\right) \cdot \sqrt{100-6^2} }{6^2-100} \times 9 = \mathbf{15.75}[/tex]
At the time the ladder is 6 feet from the wall, the area is increasing at 15.75 ft.²/sec.
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How much would you need to deposit in an account now in order to have $2000 in the account in 15
years? Assume the account earns 2% interest compounded monthly.
4000 mcmcnxmamnxmxmnxnxns
Employees at the ACME paper bag corporation have two fast food restaurant chains located next to the corporate parking lot: Carl's Jr. and Wendy's. Due to time restrictions the ACME employees eat their lunches either at Carl's Jr. or Wendy's and nowhere else. If today an employee eats lunch at Wendy's, then tomorrow the probability they'll eat lunch at Wendy's is 10% otherwise they'll eat lunch at Carl's Jr. If today an employee eats lunch at Carl's Jr., then tomorrow the probability they'll eat lunch at Carl's Jr. is 40% otherwise they'll eat lunch at Wendy's. If on Monday an employee eats lunch at Carl's Jr. what is the probability they'll eat lunch at Carl's Jr. Wednesday?
Answer:
0.7 = 70% probability they'll eat lunch at Carl's Jr. Wednesday.
Step-by-step explanation:
We have that:
Carl's Jr on Monday.
On Tuesday:
40% probability of Carl's Junior.
100 - 40 = 60% probability of Wendy's.
On Wednesday:
If on Tuesday it was on Carl's Junior, 40% probability of Carl's Junior on Wednesday.
In on Tuesday it was on Wendy's, 100 - 10 = 90% probability of Carl's Junior on Wednesday.
What is the probability they'll eat lunch at Carl's Jr. Wednesday?
[tex]p = 0.4*0.4 + 0.6*0.9 = 0.7[/tex]
0.7 = 70% probability they'll eat lunch at Carl's Jr. Wednesday.
Is the expression 6(1 + m) equal to 6 + 6m? Why or why not? How do you know?
Answer:
Yes, they are equal because of distributive property
Step-by-step explanation:
6(1 + m) = 6 + 6m
A researcher wants to test the claim that the proportion of men who watch television regularly is greater than the proportion of women who watch television regularly. She finds that 56 of 70 randomly selected men and 47 of 85 randomly selected women report watching television regularly. A 95% confidence interval for the difference in population proportions is (0.10581, 0.38831). Which of the statements gives the correct outcome of the researcher's test of the claim?A. Because the confidence interval is positive, the researcher can conclude the proportion of men and women who watch television regularly is the same.
B. Because the confidence interval is positive, the researcher can conclude the proportion of men and women who watch television regularly may be the same.
C. Because the confidence interval is positive, the researcher can conclude there is a greater proportion of women than men who watch television regularly.
D. Because the confidence interval is positive, the researcher can conclude there is a greater proportion of men than women who watch television regularly.
E. The researcher cannot draw a conclusion about a claim without performing a significance test.
Answer:
The answer is D. Because the confidence interval is positive, the researcher can conclude there is a greater proportion of men than women who watch television regularly.
Step-by-step explanation:
We can agree that the lower and upper bound of the confidence interval is positive, meaning that because the confidence interval represents the range about the difference in proportions, it being positive must mean that one of the proportions is bigger than the other. Quickly calculating the proportions shows us that men (56 / 70) watch television more frequently than women (47 / 85).
Because the confidence interval is positive, the researcher can conclude that men watch television more frequently than women. Option D is correct.
What is Statistic?The statistic is the study of mathematics that deals with relations between comprehensive data.
Here,
It is supposed to be agreed that the bottom and upper bounds of the confidence interval are positive, which means that because the confidence interval represents the range of the proportional difference, it must be positive if one of the proportions is larger than the other. Men (56 / 70) watch television more frequently than women (47 / 85), according to a quick calculation.
Thus, Because the confidence interval is positive, the researcher can conclude that men watch television more frequently than women. Option D is correct.
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I need help, I can’t seem to be o figure this out
Answer:
I'm pretty sure this is obtuse because when you add all sides it gives you 135 and it has a 90-degree angle so if it's greater than 90 it's 100% obtuse.
Step-by-step explanation:
A person places $277 in an investment account earning an annual rate of 6.7%,
compounded continuously. Using the formula V = Pem, where V is the value of the
account in t years, P is the principal initially invested, e is the base of a natural
logarithm, and r is the rate of interest, determine the amount of money, to the
nearest cent, in the account after 10 years.
9514 1404 393
Answer:
$541.32
Step-by-step explanation:
Putting the given values into the given formula, you have ...
V = P·e^(rt)
V = $277e^(0.067·10) ≈ $541.32
Find the solution of the system of equations.
6x + 2y = 16
2x - =
2y = 32
Answer:
x=6 and y=−10
Step-by-step explanation:
You can also solve this system by elimination.)
6x+2y=16;2x−2y=32
Step: Solve6x+2y=16for x:
6x+2y+−2y=16+−2y(Add -2y to both sides)
6x=−2y+16
it's proceeds
Line a is parallel to line b. If the
measure of Z2 is 78°, what is the
measure of Z8?
78° =21
314
615
78
b
This is because alternate exterior angles are congruent when we have parallel lines like this.
Angle 2 and angle 8 are both outside the parallel lines, so that's what makes them exterior angles. Also, they are on alternating sides of the transversal line (angle 2 on the left, angle 8 on the right). So that's where the "alternating" comes from. The other pair of alternate exterior angles is angle 1 and angle 7.
Write the equation of line whose b= -1 and m=5
Answer:
Step-by-step explanation:
y=mx+b
y=5x-1
Answer:
Step-by-step explanation:
use the slope intercept from of a line, where
y = mx + b
we're given m , and b
y = 5x -1
that's your answer
cuantas horas son de 7am a 7pm
Artie ate 1/5 of a box of cereal last week and 1/5 of the box more this week. How much of Arties box of cereal is left?
Karen Sue has 6 pairs of jeans that
are ripped. If that represents 40%
of the total pairs of jeans in her
wardrobe, what is the total number
of pairs of jeans in her wardrobe?
Set up as a proportion and solve.
Answer:
The total number of pairs of jeans in her wardrobe is 15.
Step-by-step explanation:
We solve this question using proportions.
6 pairs of jeans represents 40% of the total.
The total is x. Using proportions:
[tex]\frac{6}{x} = \frac{40}{100}[/tex]
[tex]\frac{6}{x} = 0.4[/tex]
[tex]0.4x = 6[/tex]
[tex]x = \frac{6}{0.4}[/tex]
[tex]x = 15[/tex]
The total number of pairs of jeans in her wardrobe is 15.
Which of the following examples has a unit rate of 70 miles per hour? Select all
that apply.
A) 210 miles in 3 hours
B) 420 miles in 6 hours
C) 280 miles in 5 hours
D) 560 miles in 8 hours
E) 560 miles in 7 hours
Answer:
A, B and D are the answers.
Answer:
A, B, D.
Step-by-step explanation:
One spring day, Jin noted the time of day and the temperature, in degrees Fahrenheit. His findings are as follows: At 6 a.m., the temperature was 56° F. For the next 5 hours, the temperature rose 1° per hour. For the next 4 hours, it rose 2° per hour. The temperature then stayed steady until 6 p.m. For the next 3 hours, the temperature dropped 1° per hour. The temperature then dropped steadily until the temperature was 62° at midnight. On the set of axes below, graph Jin's data.
Answer:
This is how the graph will look like because I don't have a graph that why I use a note
Step-by-step explanation:
At 6am it is 56°.For the next 5hours it increases to 61° since it is 1° per hour and after 4 hours again it will increase to 69° because it is 2° per hour and it stayed steady till 6pm and it dropped the next 3 hours which the temperature now reduces to 66° and dropped steadily to 62° at midnight
The temperature variations is represented on the graph attached with the answer.
What is graph?A diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.
At 6am it is 56°.For the next 5hours it increases to 61° since it is 1° per hour and after 4 hours again it will increase to 69° because it is 2° per hour and it stayed steady till 6pm and it dropped the next 3 hours which the temperature now reduces to 66° and dropped steadily to 62° at midnight
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PLEASE HELP who knows the answer to this?
Answer:
a.
Step-by-step explanation:
Kia donated a $20 bill plus 1 of
the balance in her short-term savings
account to a medical fundraiser. If Kia
donated a total of $100, how much was
in her short-term savings account?
$100 - $20 = $80
Understand?
Hi please help me i will mark as brainiest just please help!
Answer:
B
Step-by-step explanation:
Kahlil wants it to be more than 10 seconds long, and his friend wants it 5 seconds longer than that. So it has to be at least 10 + 5 seconds long or 15 seconds. B is the only option with >15, and all the possible track lengths below satisfy the inequality.
A scale model of the Washington Monument is 15 inches tall and the base is 1.5
inches wide. If the actual monument is approximately 555 feet tall, which is
closest to the width, in feet, of the base?
50
55
835
0 370
Answer:
~55 ft
Step-by-step explanation:
15/1.5 = 555(12)=12x
180x = 9990
x = 55.5
Select the null and the alternative hypotheses for the following claims:
a. "I am going to get the majority of the votes to win this election."
multiple choice 1
H0: μ = 0.50; HA: μ ≠ 0.50
H0: p ≤ 0.50; HA: p > 0.50
H0: p ≥ 0.50; HA: p < 0.50
b. "I suspect that your 10-inch pizzas are, on average, less than 10 inches in size."
multiple choice 2
H0: μ ≥ 10; HA: μ < 10
H0: p ≥ 10; HA: p < 10
H0: μ = 10; HA: μ ≠ 10
c. "I will have to fine the company since its tablets do not contain an average of 250 mg of ibuprofen as advertised."
multiple choice 3
H0: μ = 250; HA: μ ≠ 250
H0: p ≤ 250; HA: p > 250
H0: p = 250; HA: p ≠ 250
Answer:
a. H0: p ≥ 0.50; HA: p < 0.50
b. H0: μ ≥ 10; HA: μ < 10
c. H0: μ = 250; HA: μ ≠ 250
Step-by-step explanation:
a. "I am going to get the majority of the votes to win this election."
This sentence means that the probability of winning is more than fifty percent or more than half.The null hypothesis would be
H0: the probability of winning is more than 50 %
against the claim that
Ha: the probability of winning is less than 50%
So the best choice would be option c
H0: p ≥ 0.50; HA: p < 0.50
b. "I suspect that your 10-inch pizzas are, on average, less than 10 inches in size."
The claim is that the pizzas are less than 10 inches in size.
which can be written as alternate hypothesis
Ha: u < 10
so the best choice would be option a
H0: μ ≥ 10; HA: μ < 10
c. "I will have to fine the company since its tablets do not contain an average of 250 mg of ibuprofen as advertised."
In this statement the claim is that an average of ibuprofen do not contain 250 mg as advertised.
the alternate hypothesis would be u ≠ 250 mg
Ha: μ ≠ 250 and the null hypothesis is the reverse of the aalternate hypothesis.
so the best option would be part a
H0: μ = 250; HA: μ ≠ 250
Jessica has just purchased a new purse in the shape of a rectangular box to match her favorite shoes. The purse has a length of 15 cm, a width of 6.4 cm, and a height of 8 cm. What is the volume of the purse?
Adam is comparing the graphs of y=4x and y=8x. Which of the following statements is TRUE?
pls help me with this math question i beg
Answer:
All angles in a quadrilateral = 360°
b =?
b = 360 - (128 + 61 + 57)
b = 360 - 246
b = 114°
Factorise the expressions.
Answer:
Q.1 lx²+mx
=x(lx+m)
Q.2 x² - ax - bx + ab
= x(x - a) - b(x - a)
=(x - b)(x - a)
Q.3 6ab - b²+ 12ac - 2bc
= b(6a - b) - 2a(6a - b)
=(b - 2a)(6a - b)
Solve the triangle.
a = 1, b = 2, y = 70°
(Do not round until the final answer. Then round to the nearest tenth as needed.)
Answer:
cute scalene triangle.
Sides: a = 1 b = 2 c = 1.906
Area: T = 0.94
Perimeter: p = 4.906
Semiperimeter: s = 2.453
Angle ∠ A = α = 29.543° = 29°32'36″ = 0.516 rad
Angle ∠ B = β = 80.457° = 80°27'24″ = 1.404 rad
Angle ∠ C = γ = 70° = 1.222 rad
Height: ha = 1.879
Height: hb = 0.94
Height: hc = 0.986
Median: ma = 1.888
Median: mb = 1.147
Median: mc = 1.262
Inradius: r = 0.383
Circumradius: R = 1.014
Vertex coordinates: A[1.906; 0] B[0; 0] C[0.166; 0.986]
Centroid: CG[0.691; 0.329]
Coordinates of the circumscribed circle: U[0.953; 0.347]
Coordinates of the inscribed circle: I[0.453; 0.383]
Exterior (or external, outer) angles of the triangle:
∠ A' = α' = 150.457° = 150°27'24″ = 0.516 rad
∠ B' = β' = 99.543° = 99°32'36″ = 1.404 rad
∠ C' = γ' = 110° = 1.222 rad
Step-by-step explanation:
I’ll give brainliest! Can someone help me with this please!!!
Answer:
120 yards
Step-by-step explanation:
Answer:
360 ft.
Step-by-step explanation:
You multiply the number of total yards, which is 120, by 3 to get feet.
Two competing headache remedies claim to give fast-acting relief. An experiment was performed to compare the mean lengths of time required for bodily absorption of brand A and brand B headache remedies. Twelve people were randomly selected and given an oral dose of brand A and another 12 people were randomly selected and given an oral dose of brand B. The lengths of time in minutes for the drugs to reach a specified level in the blood were recorded. The mean and standard deviation for brand A was 21.8 and 8.7 minutes, respectively. The mean and standard deviation for brand B was 18.9 and 7.5 minutes, respectively. Past experience with the drug composition of the two remedies permits researchers to assume that both distributions are approximately Normal. Let us use a 5% level of significance to test the claim that there is no difference in the mean time required for bodily absorption.
Required:
Find or estimate the p — value of the sample test statistic.
Answer:
[tex]t = 0.875[/tex]
Step-by-step explanation:
Given
Brand A Brand B
[tex]n_ 1= 12[/tex] [tex]n_2 = 12[/tex]
[tex]\bar x_1 = 21.8[/tex] [tex]\bar x_2 = 18.9[/tex]
[tex]\sigma_1 = 8.7[/tex] [tex]\sigma_2 = 7.5[/tex]
Required
Determine the test statistic (t)
This is calculated as:
[tex]t = \frac{\bar x_1 - \bar x_2}{s\sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}[/tex]
Calculate s using:
[tex]s = \sqrt{\frac{(n_1-1)*\sigma_1^2+(n_2-1)*\sigma_2^2}{n_1+n_2-2}}[/tex]
The equation becomes:
[tex]s = \sqrt{\frac{(12-1)*8.7^2+(12-1)*7.5^2}{12+12-2}}[/tex]
[tex]s = \sqrt{\frac{1451.34}{22}}[/tex]
[tex]s = \sqrt{65.97}[/tex]
[tex]s = 8.12[/tex]
So:
[tex]t = \frac{\bar x_1 - \bar x_2}{s\sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}[/tex]
[tex]t = \frac{21.8 - 18.9}{8.12 * \sqrt{\frac{1}{12} + \frac{1}{12}}}[/tex]
[tex]t = \frac{21.8 - 18.9}{8.12 * \sqrt{\frac{1}{6}}}[/tex]
[tex]t = \frac{21.8 - 18.9}{8.12 * 0.408}}[/tex]
[tex]t = \frac{2.9}{3.31296}}[/tex]
[tex]t = 0.875[/tex]
What is the volume of a sphere that has a radius that measures 3 feet?
Answer:
About V≈113.1ft³
Step-by-step explanation: