Answer:
164 ft
Step-by-step explanation:
The TIME of maximum height (this is a dome shaped parabola)
will be given by t = -b/2a = - 64 / (2)(-16) = 2 sec
Putting in t = 2 into the equation will give the max height
-16 (2^2) + 64(2) + 100 = max = 164 ft
The fox observed that the tortoise plodded along at a rate of 20 meters per minute throughout the 1000-meter race.
1. Complete the table below indicating the distance traveled by the tortoise in the time elapsed.
The values that are required to complete the table above indicating the distance traveled by the tortoise in the time elapsed are calculated below.
How to calculate the distance traveled?Mathematically, the distance traveled by the tortoise would be calculated by using this formula:
Distance = speed (rate) × time
When time = 1 min, we have:
D₁ = 20 × 1
D₁ = 20 meters.
When time = 2 min, we have:
D₂ = 20 × 2
D₂ = 40 meters.
When time = 3 min, we have:
D₃ = 20 × 3
D₃ = 60 meters.
When time = 4 min, we have:
D₄ = 20 × 4
D₄ = 80 meters.
When time = 5 min, we have:
D₅ = 20 × 5
D₅ = 100 meters.
When time = 6 min, we have:
D₆ = 20 × 6
D₆ = 120 meters.
When time = 7 min, we have:
D₇ = 20 × 7
D₇ = 140 meters.
When time = 10 min, we have:
D₁₀ = 20 × 10
D₁₀ = 200 meters.
When time = 15 min, we have:
D₁₅ = 20 × 15
D₁₅ = 300 meters.
When time = 20 min, we have:
D₂₀ = 20 × 20
D₂₀ = 400 meters.
When time = 25 min, we have:
D₂₅ = 20 × 25
D₂₅ = 500 meters.
When time = 30 min, we have:
D₃₀ = 20 × 30
D₃₀ = 600 meters.
When time = 35 min, we have:
D₃₅ = 20 × 35
D₃₅ = 700 meters.
When time = 40 min, we have:
D₄₀ = 20 × 40
D₄₀ = 800 meters.
When time = 50 min, we have:
D₅₀ = 20 × 50
D₅₀ = 1,000 meters.
Learn more about distance here: brainly.com/question/10545161
#SPJ1
A complex number will, in general, have _____ fourth complex roots.
Answer:
A complex number will, in general, have five(5) fourth complex roots.
Step-by-step explanation:
We know that the nth complex roots of unity are graphically represented on a unit circle such that there are a total of n roots located at a distance by an angle of
Hence, here we are asked to find the number of complex roots of fifth complex roots.
i.e. n=5
Hence, we have five(5) fifth complex roots.
The commissioner of the state police is reported as saying that about 10% of reported auto thefts involve owners whose cars haven't really been stolen. What null and alternative hypotheses would be appropriate in evaluating this statement made by the commissioner?
A. H0: p ≥ 0.10 and H1: p < 0.10
B. H0: p ≤ 0.10 and H1: p > 0.10
C. H0: p > 0.10 and H1: p ≤ 0.10
D. H0: p = 0.10 and H1: p ≠ 0.10
The appropriate null and alternate hypotheses are (d) H0: p = 0.10 and H1: p ≠ 0.10
How to determine the hypotheses?From the question, we understand that:
The proportion of reports that have their cars stolen is given as 10%
Null hypothesis is represented with the equality sign.
So, the null hypothesis is H0: p = 0.10
The alternate hypothesis is represented with the unequal sign.
So, the alternate hypothesis is H1: p ≠0.10
Hence, the appropriate hypotheses are (d) H0: p = 0.10 and H1: p ≠ 0.10
#SPJ1
Read more about hypotheses at:
https://brainly.com/question/15980493
Nakeisha's family took a road trip to Mount Rushmore. Nakeisha fell asleep 18% of the way through the trip. If the total length of the trip was 400 miles, how many miles had they travelled when Nakeisha fell asleep?
Answer:
72 miles ....then she snored off
Step-by-step explanation:
18 % of 400 = .18 * 400 = 72 miles
I NEED HEEEEELP WITH THIS QUESTIOOOON, maybe for some people it is very easy but not for me
Answer:
the 1.5 goes between -1 and 0 and -3/2 too and -4/3 between the-2 and the 3/2 between the 0 and 1
Step-by-step explanation:
Graph the function with the following domain and range domain 0,1,2,3 and range -3,0,5
Answer:
hope this is what you ask for and i hope it helps
Step-by-step explanation:
find KM ( SHOW YOUR WORK )
Test the claim that LeBron James and Steph Curry average the same amount of points per game, on average.
Be sure to include the claim, critical values, test statistic and the conclusion.
For 70 games Lebron James averaged 30.1 points with a standard deviation of 9.112
For 70 games Steph Curry averaged 25.5 points with a standard deviation of 12.602
When the variances are known and the sample size is high, a z-test is used to assess if two population means vary. The mean of the two players is not the same.
What is a Z-test?When the variances are known and the sample size is high, a z-test is used to assess if two population means vary.
In order to execute an appropriate z-test, the test statistic is expected to have a normal distribution, and nuisance factors such as standard deviation should be known.
(1) Null and Alternative Hypotheses
The following null and alternative hypotheses need to be tested:
[tex]\begin{array}{ccl} H_0: \mu_1 & = & \mu_2 \\\\ H_a: \mu_1 & \ne & \mu_2 \end{array}[/tex]
This corresponds to a two-tailed test, and a z-test for two means, with known population standard deviations, will be used.
(2) Rejection Region
Based on the information provided, the significance level is α=0.05, and the critical value for a two-tailed test is [tex]z_c = 1.96[/tex]
The rejection region for this two-tailed test is R={z:∣z∣>1.96}
(3) Test Statistics
The z-statistic is computed as follows:
[tex]\begin{array}{ccl} z & = & \displaystyle \frac{\bar X_1 - \bar X_2}{\sqrt{ {\sigma_1^2/n_1} + {\sigma_2^2/n_2} }} \\\\ & = & \displaystyle \frac{ 30.1 - 25.5}{\sqrt{ {9.112^2/70} + {12.602^2/70} }} \\\\ & = & 2.475 \end{array}[/tex]
[tex]\begin{array}{ccl} z & = & \displaystyle \frac{\bar X_1 - \bar X_2}{\sqrt{ {\sigma_1^2/n_1} + {\sigma_2^2/n_2} }} \\\\ & = & \displaystyle \frac{ 30.1 - 25.5}{\sqrt{ {9.112^2/70} + {12.602^2/70} }} \\\\ & = & 2.475 \end{array}[/tex]
(4.) The decision about the null hypothesis
Since it is observed that |z| = 2.475 > z_c = 1.96, it is then concluded that the null hypothesis is rejected.
Using the P-value approach: The p-value is p = 0.0133p=0.0133, and since p = 0.0133 < 0.05p=0.0133<0.05, it is concluded that the null hypothesis is rejected.
(5.) As it is concluded that the null hypothesis H₀ is rejected. Therefore, there is enough evidence to claim that the population mean μ1 is different than μ2.
Hence, the mean of the two players is not the same.
Learn more about Z-test:
https://brainly.com/question/15683598
#SPJ1
A party hat shaped like a cone requires about 66 square inches ( Surface Area ) of paper to make. If the slant height is 7 inches, how wide is the hat?
Answer:
6 inches
Step-by-step explanation:
Solving
Curved Area = π x r x slant height66 = 3.14 x 7 x rr = 66/21.98 ≅ 3 inchesWidth of the hat
Diameter of the cone2 x Radius2 x 3 = 6 inchesAnswer:
6.00 in (nearest hundredth)
Step-by-step explanation:
Lateral surface area = surface area excluding the bases(s)
Lateral surface area of a cone = [tex]\pi rs[/tex]
(where r is the radius and s is the slant height)
Given:
lateral surface area ≈ 66 in²slant height (s) = 7 in[tex]\implies 66= \pi r \cdot 7=7 \pi r[/tex]
[tex]\implies r=\dfrac{66}{7 \pi}[/tex]
The width of the hat is the diameter. As diameter = 2r:
[tex]\begin{aligned}\implies \textsf{width} & =2 \cdot \dfrac{66}{7 \pi}\\\\ & =\dfrac{132}{7 \pi}\\\\ & = 6.00\: \sf in\:(nearest\:hundredth)\end{aligned}[/tex]
What negative impact can interdependence have on a country?
A. Threat to political interference
B. Threat to security
C. Threat to industrialization
D. Increased progress and industrialization
Suppose you draw a card from a well-shuffled deck of 52 cardsWhat is the probability of drawing a 2 or a queen?
[tex]\frac{2}{13}[/tex]
Step-by-step explanation:Probability is finding the chance that some specific outcome will occur. In this case, we are looking for the probability of one of two outcomes.
Equally Likely Outcomes
When drawing a card from a well-shuffled deck, all outcomes (cards) are equally likely to be drawn. Each card was a 1/52 probability of occurring.
Probability of Two Outcomes
In a deck of cards, there are 4 cards of each number. This means that the probability of drawing a 2 is 4/52, the same for a queen.
So, to find the probability of one of the two desired outcomes is equal to adding the probabilities together.
[tex]\frac{4}{52} +\frac{4}{52} =\frac{8}{52}[/tex]This fraction can then be simplified further:
[tex]\frac{2}{13}[/tex]A fictional country has a population of 5 million people and a net immigration rate of 1 person per 1000 people. The population is increasing only due to migration and not biological replacement. How long will it take the country’s population to double?
Group of answer choices
300 years
1,000 years
5,000 years
700 years
Answer:
1,000
Step-by-step explanation:
just took the quiz
The area of a rectangular patio is 24 3/8
square meters. The width of the patio is 3 3/4
meters. What is the length? Enter your answer as a mixed number in simplest form.
The length of the patio is ___ meters.
Answer:
6 1/2
Step-by-step explanation:
Use the area formula: A=LengthxWidth
Plug in what we know: 24 3/8= 3 3/4x Width
We need to isolate the width; get it by itself.
Do this by (24 3/8)/(3 3/4). The best way is to enter this into a calculator.
Your answer is 6 1/2
Which term describes the set of all possible outcomes for a probability event? A. Sample space B. Empirical probability C. Elements OD. Likelihood
Answer:
Sample Space
Step-by-step explanation:
Giving brainliest :D (show steps in a simple way ty!)
Answer:
5xsquared+x+5
Step-by-step explanation:
first combine x squared with 4x squared and you will get 5xsquared.
next combine 6x and -5x and you will get 1x or just simply x. Finally combine 3 and 2 (3+2) = 5.
The highest mark in the Science test was 74. Three students scored 49 which was five marks higher than the lowest score. What was the range of scores?
Answer:
25
Step-by-step explanation:
you subtract the highest number
Answer:
The "range" of a set of numbers is just the difference between the biggest number and the smallest number. (The maximum "far-apart-ness" of the scores).
Hope this helps you!!
Don't forget to mark me Brainleast!!!!!!!!!!!!
Thankyou for joining Brainly Community!!!!!!!
what is 9x-2=(3x+9) + (5x) ?
Need to show work for limits
Answer:
[tex]\displaystyle \lim_{x \to -\infty} (-7x^5 + x^3) = \infty[/tex]
General Formulas and Concepts:
Calculus
Limits
Limit Rule [Variable Direct Substitution]:
[tex]\displaystyle \lim_{x \to c} x = c[/tex]
Step-by-step explanation:
Step 1: Define
Identify given.
[tex]\displaystyle \lim_{x \to -\infty} (-7x^5 + x^3)[/tex]
Step 2: Evaluate
[Limit] Apply Limit Rule [Variable Direct Substitution]:Recall that x⁵ is a "faster" function than x³. Also recall that we have 2 negatives, which would turn positive. Therefore, we can ignore the 2nd part of the limit and focus on the first:
[tex]\displaystyle \begin{aligned}\lim_{x \to -\infty} (-7x^5 + x^3) & = -7(- \infty)^5 + (- \infty)^3 \\& = -7(- \infty)^5 \\& = -7(- \infty) \\& = 7(\infty) \\& = \boxed{\infty} \\\end{aligned}[/tex]
∴ we have found the limit to equal infinity.
---
Learn more about limits: https://brainly.com/question/27438198
Learn more about calculus: https://brainly.com/question/27351658
---
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Find the standard equation of the circle with center (5, -3
and with a point on the circle (-3,3)
Answer:
○ C
Explanation:
Accourding to one of the circle equations, [tex]\displaystyle (x - h)^2 + (y - k)^2 = r^2,[/tex]the centre of the circle is represented by [tex]\displaystyle (h, k).[/tex]Moreover, all negative symbols give you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must pay cloce attention to which term gets which symbol. Another thing you need to know is that the radius will ALWAYS be squared, so no matter how your equation comes about, make sure that the radius is squared. Now, in case you did not know how to define the radius, you can choose between either method:
Pythagorean Theorem
[tex]\displaystyle a^2 + b^2 = c^2 \\ \\ 6^2 + 8^2 = r^2 \hookrightarrow 36 + 64 = r^2 \hookrightarrow \sqrt{100} = \sqrt{r^2} \\ \\ \boxed{10 = r}[/tex]
Sinse we are dealing with length, we only desire the NON-NEGATIVE root.
Distanse Equation
[tex] \displaystyle \sqrt{[-x_1 + x_2]^2 + [-y_1 + y_2]^2} = d \\ \\ \sqrt{[-5 - 3]^2 + [3 + 3]^2} = r \hookrightarrow \sqrt{[-8]^2 + 6^2} = r \hookrightarrow \sqrt{64 + 36} = r; \sqrt{100} = r \\ \\ \boxed{10 = r}[/tex]
Sinse we are dealing with distanse, we only desire the NON-NEGATIVE root.
I am joyous to assist you at any time.
Create an equation that describes the greatest horizontal length, H, in terms of the greatest vertical length, V.
The equation that describes the greatest horizontal length, H, in terms of the greatest vertical length, V is H = 2V + 3.
How to compute the equation?Your information is incomplete. Therefore, an overview will be given.
Let's assume that the value of the horizontal length is 3 plus twice the value of the the vertical length. This will be:
H = (2 × V) + 3
H = 2V + 3
In conclusion, the equation is H = 2V + 3.
Learn more about equations on:
https://brainly.com/question/2972832
Given sides a-10, b=5 and angle ZA-100°. Find the corresponding value for ZB. Options: A 60° B 5° D -29.5° C 29.5°
The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. The measure of the ∠B=29.5°.
What is Sine rule?The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. It is given by the formula,
[tex]\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ A}{\beta} =\dfrac{Sin\ A}{\gamma}[/tex]
where Sin A is the angle and α is the length of the side of the triangle opposite to angle A,
Sin B is the angle and β is the length of the side of the triangle opposite to angle B,
Sin C is the angle and γ is the length of the side of the triangle opposite to angle C.
Given that sides a=10, b=5 and the measure of the ∠A=100°. Therefore, the using the sine law,
[tex]\rm \dfrac{Sin\ A}{a} = \dfrac{Sin\ B}{b}[/tex]
[tex]\rm \dfrac{Sin\ 100^o}{10} = \dfrac{Sin\ B}{5}\\\\\rm \dfrac{(Sin\ 100^o) \times 5}{10} = Sin\ B\\\\Sin\ B = 0.04924\\\\\angle B = 29.498^o \approx 29.5^o[/tex]
Hence, the measure of the ∠B=29.5°.
Learn more about Sine Rule:
https://brainly.com/question/17289163
#SPJ1
The price of an item has been reduced by $3.49. The new sale price is $31.38. What was the original price?
Add the amount it was reduced to the new price:
3.49 + 31.38 = 34.87
Original price = $34.87
Answer:
When finding the unknown original price, add the sale reduction to the new sale price to get the old sale price.
[tex]3.49 + 31.38 = 34.87[/tex]
Therefore, the original sales price was 34.87
Wen painted 3/10 of her living room yesterday and 4/10 to today. What fraction of the room has she painted so far?
Answer:
7
Step-by-step explanation:
3/10+4/10 =7/10
Answer:
7/10, or 70%
Step-by-step explanation:
You just add the fractions together and get 7/10. You could also find a common denominator and the add them together. You would do, 9/30+ 12/30= 21/30, or 7/10.
the hooded men rushed out of town at 100 miles per hour one hour later the masked men left town in pursuit at 125 mph how many hours did it take the masked men to catch up to the hooded men
Answer:
It took 12.5 hours to catch up with the men
Question:
the hooded men rushed out of town at 100 miles per hour one hour later the masked men left town in pursuit at 125 mph how many hours did it take the masked men to catch up to the hooded men
Answer:
12.5
Step-by-step explanation:
This doesn't say it in the question but the hooded man drove 125 miles,
his speed was 100 mph.
The masked man drove also drove 125 miles but he drove at 125 mph.
Ok sorry lets make this simpler.
divide 1250 by 100 and your answer is:
12.5
So, it took the masked man 12.5 hours to catch up with the hooded man.
Please help and explain this to me!! I am confused and would like to know how to solve!!
Answer:
The sum of the numerators is incorrect.
The one where -1/2 is the final answer.
Step-by-step explanation:
-5/8 + 1/8 does equal (-5 + 1)/8. However, -5 + 1 is not equal to -6. It is equal to -4. -4/8 would simplify down to -1/2, which is the correct answer.
i would like the answer to 1/4 minus 1/3 is it 12
Answer:
-1/12
Step-by-step explanation:
1/4 - 1/3 = 3/12 - 4/12 = - 1/12
The volume of a rectangular prism is
300 in. If the length is 10in, the width
is 2 in, what is the height?
Answer:
The Height is 15in
Step-by-step explanation:
V=L.W.H
300=10x2xH
300=20xH
300/20=H
H=15in
I need help with my geometry homework.
Step-by-step explanation:
5x + 80 = 180
x = 20
2x = 40
3x=60
7x=140
Use 2-3 sentences to explain, in your own words, the difference between an angle of elevation and an angle of depression. Use geometry vocabulary.
To be able to buy a new computer, Yoko decides to save for 5 years. She opens a savings account with $400. The account pays simple interest at an annual rate of 2%. She doesn't make any more deposits.
(a) How much total interest will Yoko earn?
(b) What will the total amount in the account be (including interest)?
Answer:
A) $40 total interest
B) $440