PLEASE HELP
8.07a, part 1
1. Find the vertex, focus, directrix, and focal width of the parabola. (1 point)
negative 1 divided by 40 x squared equals y
A) Vertex: (0, 0); Focus: (0, -10); Directrix: y = 10; Focal width: 160
B) Vertex: (0, 0); Focus: (-20, 0); Directrix: x = 10; Focal width: 160
C) Vertex: (0, 0); Focus: (0, -10); Directrix: y = 10; Focal width: 40
D) Vertex: (0, 0); Focus: (0, 10); Directrix: y = -10; Focal width: 10
2. Find the standard form of the equation of the parabola with a focus at (0, -2) and a directrix at y = 2.
A)y2 = -2x
B) y2 = -8x
C) y equals negative 1 divided by 8 x squared
D) y equals negative 1 divided by 2 x squared
3. Find the standard form of the equation of the parabola with a focus at (-8, 0) and a directrix at x = 8.
A) y equals negative 1 divided by 32 x squared
B) y2 = 16x
C) 16y = x2
D) x equals negative 1 divided by 32 y squared
4. A building has an entry the shape of a parabolic arch 84 ft high and 42 ft wide at the base, as shown below.
A parabola opening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 84 feet and its width from left to right is 42 feet.
Find an equation for the parabola if the vertex is put at the origin of the coordinate system.
A) y2 = -21x
B) x2 = -21y
C) x2 = -5.3y
D) y2 = -5.3x
5. Find the center, vertices, and foci of the ellipse with equation x squared divided by 81 plus y squared divided by 225 equals 1 .
A) Center: (0, 0); Vertices: (-15, 0), (15, 0); Foci: (0, -9), (0, 9)
B) Center: (0, 0); Vertices: (0, -15), (0, 15); Foci: (-9, 0), (9, 0)
C) Center: (0, 0); Vertices: (0, -15), (0, 15); Foci: (0, -12), (0, 12)
D) Center: (0, 0); Vertices: (-15, 0), (15, 0); Foci: (-12, 0), (12, 0)
6. Find the center, vertices, and foci of the ellipse with equation 2x2 + 8y2 = 16.
A) Center: (0, 0); Vertices: the point zero comma negative two square root two and the point zero comma 2 square root two ; Foci: Ordered pair 0 comma negative square root 6 and ordered pair 0 comma square root 6
B) Center: (0, 0); Vertices: (-8, 0), (8, 0); Foci: Ordered pair negative 2 square root 15 comma 0 and ordered pair 2 square root 15 comma 0
C) Center: (0, 0); Vertices: (0, -8), (0, 8); Foci: Ordered pair 0 comma negative 2 square root 15 and ordered pair 0 comma 2 square root 15
D) Center: (0, 0); Vertices: the point negative square root six comma zero and the point square root six comma zero ; Foci: Ordered pair negative square root 6 comma 0 and ordered pair square root 6 comma 0
7. Graph the ellipse with equation x squared divided by 36 plus y squared divided by 49 equals 1 .
A) A horizontal ellipse is shown on the coordinate plane centered at the origin with vertices at the point negative seven comma zero and the point seven comma zero. The minor axis has endpoints at zero comma six and zero comma negative six.
B) A vertical ellipse is shown on the coordinate plane centered at the origin with vertices at the point zero comma seven and zero comma negative seven. The minor axis has endpoints at negative six comma zero and six comma zero.
C) A horizontal ellipse is shown on the coordinate plane centered at (6, 7) with vertices at (–1, 7) and (13, 7) and minor axis endpoints at (6, 13) and (6, 1).
D) A horizontal ellipse is shown on the coordinate plane centered at the point six comma seven with vertices at the point negative one comma seven and thirteen comma seven. The minor axis has endpoints at six comma thirteen and six comma one.
8. Find an equation in standard form for the ellipse with the vertical major axis of length 10 and minor axis of length 8.
A) x squared divided by 25 plus y squared divided by 16 equals 1
B) x squared divided by 5 plus y squared divided by 4 equals 1
C) x squared divided by 4 plus y squared divided by 5 equals 1
D) x squared divided by 16 plus y squared divided by 25 equals 1
9. Find the vertices and foci of the hyperbola with equation quantity x plus 5 squared divided by 36 minus the quantity of y plus 1 squared divided by 64 equals 1 .
A) Vertices: (-1, 3), (-1, -13); Foci: (-1, -13), (-1, 3)
B) Vertices: (3, -1), (-13, -1); Foci: (-13, -1), (3, -1)
C) Vertices: (-1, 1), (-1, -11); Foci: (-1, -15), (-1, 5)
D) Vertices: (1, -1), (-11, -1); Foci: (-15, -1), (5, -1)
Vertex: (0, 0); Focus: (0, -10); Directrix: y = 10; Focal width: 10
2. C) y equals negative 1 divided by 8 x squared
3. D) x equals negative 1 divided by 32 y squared
4. C) x2 = -5.3y
5. C) Center: (0, 0); Vertices: (0, -15), (0, 15); Foci: (0, -12), (0, 12)
6. None from the choices, it should be
Center: (0, 0); Vertices: the point negative two square root two comma zero and the point 2 square root two comma zero; Foci: Ordered pair negative square root 6 comma zero and ordered pair square root 6 comma zero
7. B) A vertical ellipse is shown on the coordinate plane centered at the origin with vertices at the point zero comma seven and zero comma negative seven. The minor axis has endpoints at negative six comma zero and six comma zero.
8. D) x squared divided by 16 plus y squared divided by 25 equals 1
9. D) Vertices: (1, -1), (-11, -1); Foci: (-15, -1), (5, -1)
Answer:
the answer is letter C
Step-by-step explanation:
Raina is fertilizing her garden. The garden is in the shape of a rectangle. Its length is
15 feet and its width is 13
feet. Suppose each bag of fertilizer covers 39
square feet. How many bags will she need to cover the garden?
Answer: 5 bags
Step-by-step explanation:
The set of life spans of an appliance is normally distributed with a mean mc013-1.jpg = 48 months and a standard deviation mc013-2.jpg = 8 months. What is the life span of an appliance that has a z-score of –3?
The life span of an appliance that has a z-score of –3 is 24 months if the set of life spans of an appliance is normally distributed with a mean is 48 months and a standard deviation is 8 months.
What is Z-test?The Z test is a parametric procedure that is used on data that is dispersed in a normal fashion. For testing hypotheses, the z test can be used on one sample, two samples, or proportions. When the population variance is known, it analyzes if the means of two big groups are dissimilar.
We have:
Z = -3,
[tex]\rm \mu = 48[/tex]
[tex]\sigma = 8[/tex]
We know the formula for the Z-score:
[tex]\rm Z = \frac{X-\mu}{\sigma}[/tex]
[tex]\rm-3= \frac{X-48}{8}[/tex]
-24 = X - 48
X = 24 months
Thus, the life span of an appliance that has a z-score of –3 is 24 months if the set of life spans of an appliance is normally distributed with a mean is 48 months and a standard deviation is 8 months.
Learn more about the Z-test here:
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Lines are perpendicular when the slopes are _____
what is the fourth term of the expansion of the binomial (2x+5)^5
when expanded from left to right the powers of x decrease from 5 to 0 and powers of y increase from 0 to 5
substitute x =2x and y = 5
(2x + 5)⁵ = (2x)⁵ + 5(2x)⁴5 + 10(2x)³5² + 10(2x)²5³ + 5(2x)5⁴ + 5⁵
= 32x⁵ + 400x⁴ + 2000x³ + 5000x² + 6250x + 3125Find the length of JK and the measure of M. A. JK=26, m=33 B. JK=26, M=54. C. JK=33, M=26. D. JK=54, M=33
Answer:
c i would think/suppose
Step-by-step explanation:
helppppppppppppppppppp
Please help?
What is m V?
Round only your final answer to the nearest tenth.
The answer would be 53.9
The picture below shows a portion of a river dam:
Which of the following can be used to calculate the height of the river dam? (6 points)
220 cos 40°
220 divided by tan 40 degrees
220 sin 40°
220 divided by cos 40 degrees
Answer:
220cos40
Step-by-step explanation:
cos40=x/220
(220)cos40=x/220(220)
220cos40=x
A harris poll found that 35% of people said that they drink a caffeinated beverage to combat midday drowsiness. a recent survey found that 19 out of 48 randomly selected people stated that they drank a caffeinated beverage to combat midday drowsiness. at latex-8e4a9cff882bfbfe876f36fb5b4c08e8_5a945b8082ee7.png, is the claim of the percentage found in the harris poll believable?
To determine the believability of the Harris Poll's claim that 35% use caffeine to combat drowsiness, a hypothesis test for proportions is needed. The sample proportion of 39.58% from the recent survey would be tested against the null hypothesis of 35% using a z-score calculation. Depending on if the z-score falls within the critical region, we can either reject or fail to reject the null hypothesis.
Explanation:To determine if the claim of the percentage found in the Harris Poll is believable based on the recent survey, we can conduct a hypothesis test for proportions. The null hypothesis (¿¿H₀) is that the true proportion of people who drink a caffeinated beverage to combat midday drowsiness is 35%, as stated by the Harris Poll. The alternative hypothesis (¿¿H₁) would be that the true proportion is different from 35%.
We use the information that 19 out of 48 randomly selected people stated that they drank a caffeinated beverage for midday drowsiness, which gives us a sample proportion of approximately 39.58%. To test this, we can calculate the z-score for the sample proportion and compare it to the critical value for α = 0.05 (two-tailed test). If the calculated z-score falls within the critical region, we reject the null hypothesis, indicating that the Harris Poll's claim is not believable. However, if the z-score is outside the critical region, we do not have enough evidence to reject the null hypothesis, and thus the claim is considered believable.
To perform this test, we would need to calculate the standard error for the proportion, z-score, and then compare the z-score to the appropriate critical value. Without performing the calculations here, we cannot definitively conclude about the believability of the Harris Poll's percentage claim. However, a statistician would run these numbers to reach a conclusion.
Summer looked at the formula for the Pythagorean Theorem, ashe said that it didn't matter which sides of a right triangle were a, b, and C. Is she correct?
ALL I NEED YOU GUYS TO DO IS TO EXPLAIN THIS IN THE MOST FANCY WAY POSSIBLE!!!! THIS IS JUST FOR FUN, I WILL MARK BRAINLIEST FOR THE FANCIEST ANSWER!!!!
WHAT IS 5x5?!?!?!?!?!
It's 25 easy how I got my answer I looked on my fingers and put 5 fingers up and i did it 5 times and got 5.10.15.20.25 that's 5 times
An amount of $27,000 is borrowed for 11 years at 8.25%
interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?
Use the calculator provided and round your answer to the nearest dollar.
in a club there are 10 women and 10 men. A comittee of 3 men and 2 women is to be chosen. how many different possibilities are there?
Find the Area of the figure
What is the area of the shaded region of the following figure?
446 in.2
5,760 in.2
4,788 in.2
5,274 in.2
Answer:
5,274 in.2
Step-by-step explanation:
Find the area of both the shaded and not shaded regions.
Shaded: 8 ft x 12 in = 96 5 ft x 12 in = 60
Then: 96 in x 60 in = 5760
Not Shaded: 27 in x (36 / 2) 18 in = 486
Then Subtract The Not Shaded Region From The Shaded Region:
5,760 - 486 = 5,274
what is the approximate area of the shaded region
In a circle with a radius of 6 m, an arc is intercepted by a central angle of 7π4 radians.
What is the arc length?
Use 3.14 for π .
Answer:
Arc length = 32.97 m .
Step-by-step explanation:
Given : In a circle with a radius of 6 m, an arc is intercepted by a central angle of 7π/4 radians and use 3.14 for π .
To find : What is the arc length.
Solution : We have given a circle of radius = 6 m
Central angle = 7π/4
Formula of arc length = radius × central angle .
Arc length = 6 × ([tex]\frac{7(3.14)}{4}[/tex]).
Arc length = 32.97 m .
Therefore, Arc length = 32.97 m .
Devin borrowed $1,058 at 13 percent for nine months. What will he pay in interest?
A. 103.16
B.105.80
C.137.54
D.122.40
Devin borrowed $1,058 at 13 percent for nine months.
We have to calculate the interest paid.
Interest = [tex] \frac{P \times R \times T}{100} [/tex]
Substituting the values of
Principal = $1058
Rate = 13%
Time = 9 months = [tex] \frac{9}{12} [/tex] year
Interest = [tex] \frac{1058 \times 13 \times 9}{12 \times 100} [/tex]
Interest = 103.155
= 103.16
So, Devin will pay 103.16 as the interest.
Therefore, Option A is the correct answer.
What is the area of this triangle?
A=bh2
24 in²
30 in²
48 in²
96 in²
Right triangle with height labeled 8 inches, base labeled 6 inches, and third side labeled 10 inches.
While hovering near the top of a waterfall in a national park at 46244624 feet, a helicopter pilot accidentally drops his sunglasses. the height h left parenthesis t right parenthesish(t) of the sunglasses after t seconds is given by the polynomial function h left parenthesis t right parenthesis equals negative 16 t squared plus 4624h(t)=−16t2+4624. when will the sunglasses hit the ground?
If f(x) = 6x - 4, what is f(x) when x = 8?
after earning $17 in interest bob bank account has $143 how many dollars were in the account to start with
a) The volleyball reached its maximum height after 3 seconds.
b) The maximum height of the volleyball was 23 feet.
c) If the volleyball is not returned by the opposing team, it will hit the ground in
5.5 seconds.
d)The graph that models the volleyball's height over time is exponential.
e) The volleyball was served for a height of 5 feet.
Charley wants to have $950,000 when he retires in a year. If he currently has $900,000 to put in a 1-year CD, which of these APRs and compounding periods will allow him to reach his goal?
A. An APR of 5.44% compounded semiannually
B. An APR of 5.42% compounded monthly
C. An APR of 5.34% compounded daily
D. An APR of 5.43% compounded quarterly
Charley needs an APR of 5.44% compounded semiannually to reach his goal of $950,000 in a year.(A)
Given:
Final Amount (A) = $950,000
Principal Amount (P) = $900,000
Time (t) = 1 year
We use the compound interest formula: A = [tex]P(1 + r/n)^{(nt)[/tex]
Option A: 5.44% APR compounded semiannually
APR (r) = 0.0544
Compounding periods per year (n) = 2
Plugging in the values, we get: A = 900,000[tex](1 + 0.0544/2)^{(2*1)[/tex]≈ $949,999 (which is approximately $950,000)
Option B: 5.42% APR compounded monthly
APR (r) = 0.0542
Compounding periods per year (n) = 12
Plugging in the values, we get: A = 900,000[tex](1 + 0.0542/12)^{(12*1)[/tex] ≈ $949,941 (less than $950,000)
Option C: 5.34% APR compounded daily
APR (r) = 0.0534
Compounding periods per year (n) = 365
Plugging in the values, we get: A = 900,000[tex](1 + 0.0534/365)^{(365*1)[/tex] ≈ $949,591 (less than $950,000)
Option D: 5.43% APR compounded quarterly
APR (r) = 0.0543
Compounding periods per year (n) = 4
Plugging in the values, we get: A = 900,000[tex](1 + 0.0543/4)^{(4*1)[/tex] ≈ $949,980 (missing the goal by a small amount)
Conclusion: The correct option is 5.44% compounded semiannually as it allows Charley to reach his goal of $950,000.
A circular test track for cars has a circumference of 2.7km . A car travels around the track from the southernmost point to the northernmost point. What distance does the car travel? (answer 1.35km). Part B !!!!!!!What is the car's displacement from its original position?,
is this a linear function , why or why not ? explain
y=x^2-1
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