Distance = √[ ( 7 - 3 )^2 + ( 2p - 0 )^2 ]
Distance = √(4)^2 + ( 2p)^2
Distance = √16 + 4p^2
As the question said : Distance = √80
√80 = √16 + 4p^2
Thus :
16 + 4p^2 = 80
Subtract both sides 16
16 - 16 + 4p^2 = 80 - 16
4p^2 = 64
Divide both sides by 4
4p^2 ÷ 4 = 64 ÷ 4
p^2 = 16
Thus :
p = 4 or p = - 4
What constant acceleration is required to increase the speed of a car from 30 miyh to 50 miyh in 5 seconds?
Answer:
The acceleration is 1.8 m/s^2.
Step-by-step explanation:
initial velocity, u = 30 mph = 13.4 m/s
Final velocity, v = 50 mph = 22.4 m/s
time, t = 5 s
Let the acceleration is a.
Use first equation of motion
v = u + at
22.4 = 13.4 + 5 a
a = 1.8 m/s^2
a test for diabetes results in a positive test in 95% of the cases where the disease is present and a negative test in 07% of the cases where the disease is absent. if 10% of the population has diabetes, what is the probability that a randomly selected person has diabetes, given that his test is positive
Answer:
0.9378 = 93.78% probability that a randomly selected person has diabetes, given that his test is positive.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Positive test
Event B: Person has diabetes.
Probability of a positive test:
0.95 out of 0.1(person has diabetes).
0.007 out of 1 - 0.1 = 0.9(person does not has diabetes). So
[tex]P(A) = 0.95*0.1 + 0.007*0.9 = 0.1013[/tex]
Probability of a positive test and having diabetes:
0.95 out of 0.1. So
[tex]P(A \cap B) = 0.95*0.1 = 0.095[/tex]
What is the probability that a randomly selected person has diabetes, given that his test is positive?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.095}{0.1013} = 0.9378[/tex]
0.9378 = 93.78% probability that a randomly selected person has diabetes, given that his test is positive.
father of economics
A poll of 2,060 randomly selected adults showed that 89% of them own cell phones. The technology display below results from a test of the claim that 91% of adults own cell phones. Use the normal distribution as an approximation to the binomial distribution, and assume a 0.01 significance level to complete parts (a) through (e).
Test of p=0.91 vs p≠0.91
Sample X N Sample p 95% CI Z-Value p-Value
1 1833
2,060 0.889806 ( 0.872035 , 0.907577 ) ~ 3.20 0.001
a. Is the test two-tailed, left-tailed, or right-tailed?∙
Left-tailed test∙
Two-tailed test∙
Right tailed test
b. What is the test statistic?
The test statistic is _____ (Round to two decimal places as needed.)
c. What is the P-value?
The P-value is _____ (Round to three decimal places as needed.)
d. What is the null hypothesis and what do you conclude about it?
Identify the null hypothesis.
A. H0:p<0.91∙
B. H0:p≠0.91∙
C. H0:p>0.91∙
D. H0:p=0.91.
Answer:
Two tailed test
Test statistic = 3.20
Pvalue = 0.001
H1 : p ≠ 0.91
Step-by-step explanation:
Given :
Test of p=0.91 vs p≠0.91
The use if not equal to ≠ sign in the null means we have a tow tailed test, which means a difference exists in the proportion which could be lesser or greater than the stated population proportion.
The test statistic :
This is the Z value from the table given = 3.20
The Pvalue = 0.001
Since Pvalue < α ;Reject H0
The total amount of time university students in the United States spend sleeping grooming, eating and drinking, and traveling is about Average weekday time use for full-time college and university students in the US Sleeping 36.2% Leisure and sports 17.19% 3.3% 4.2% Grooming 13.8% 5.8% Eating and drinking Educational activities 10.0% 9.696 Traveling Other Work and related activities
Answer:
yes
Step-by-step explanation:
The total amount of time university students in the United States spend sleeping, eating and drinking, and doing leisure and sports is about: Average weekday time used for full-time college and university students in the US Sleeping 36.2% Leisure and sports 17.1% 3.3% Grooming 4.2% Eating and drinking 13.8% 5.8% Educational activities 9.6% Traveling 10.0% Other Work and related activities A A 1/3 of their total time 3/5 of their total time C) 1/2 of their total time 3/4 of their total time
How many hours of sleep does a typical college student get on a weekday?"Our data was consistent with what researchers have found in academic studies — that students are in bed, on average, seven to eight hours per weeknight," says Brian Wilt, Jawbone's head of data science and analytics.
How much time does the average college student spend sleeping?On average, college students get a whopping six hours of sleep a night according to a study by the University of Georgia. Lack of sleep can take a toll on your mental health, cause a reduction in cognitive performance and affect your memory capacity!
Learn more about the average college student spend sleeping at
https://brainly.com/question/14448167
#SPJ2
Your help is very much appreciated I will mark brainliest:)
Answer:
B. Yes. By SSS~
Step-by-step explanation:
From the diagram given, we have the corresponding sides of both triangles as follows:
RQ/KL = 24/20 = 6/5
QP/LM = 18/15 = 6/5
RP/KM = 12/10 = 6/5
From the above, we can see that the ratio of the corresponding side lengths of both triangles are equal. This means that all three sides of one triangle are proportional to all corresponding sides of the other triangle.
The SSS similarity theorem states that if all sides of one triangle are proportional to all corresponding sides of another, then both triangles are similar to each other.
Therefore, ∆KLM ~ ∆RQP by SSS similarity.
Need it done ASAP please help
Answer:
[tex]M_{st} = (\frac{-2+4}{2}, \frac{-4+6}{2})[/tex]
[tex]M_{st}=(\frac{2}{2}, \frac{2}{2} )[/tex]
[tex]M_{st}=(1, 1)[/tex]
[tex]M_{cd}=(\frac{-6+4}{2} , \frac{10-8}{2} )[/tex]
[tex]M_{cd}=(\frac{-2}{2} , \frac{2}{2} )[/tex]
[tex]M_{cd}=(-1, 1)[/tex]
What is the product?
Answer:
Step-by-step explanation:
[tex]\begin{bmatrix}3 & 6 & 1\\ 2 & 4& 0\\ 0 & 6 & 2\end{bmatrix}\times\begin{bmatrix}2\\ 0\\ 1\end{bmatrix}[/tex]
Multiply the terms of the rows of the first matrix with the terms given in the column of the second matrix.
[tex]=\begin{bmatrix}(3\times 2+6\times 0+1\times 1)\\ (2\times 2+4\times 0+0\times1)\\ (0\times 2+6\times 0+2\times 1)\end{bmatrix}[/tex]
[tex]=\begin{bmatrix}7\\ 4\\ 2\end{bmatrix}[/tex]
Bryce grew 3 1/2 inches each year for the past 4 years. How many inches total has Bryce grown in the past 4 years?
Answer:
14
Step-by-step explanation:
3 1/2 multiply by 4 equals 14
Các mô hình h i quy sau đây có ph i mô hình tuy n tính hay không? N u là môồảếếhình h i quy phi tuy n, hãy đ i v mô hình h i quy tuy n tính?ồếổềồếa) iiiuXY++=21lnββb) iiiuXY++=lnln21ββc) iiiuXY++=1ln21ββd) eiiuXiY++=21ββe) eiiu
need help asap
what is the value of f(3) in the function below
Answer:
Step-by-step explanation:
The given function is :
Here , x= independent variable where we place the input value and f(x) = dependent variable where we get the output value.
Now , when we put x= 3 , we get
That means , the value of f(3) in the given function is 8.
Hence, the correct answer is B=8.
X+y=11
Graphing which function
Answer:
Step-by-step explanation:
slopee -1
y-intercept (0,11)
x y
0 11
1 10
Instructions: Given the following constraints, find the maximum and minimum values for
z
.
Constraints: 2−≤124+2≥0+2≤6 2x−y≤12 4x+2y≥0 x+2y≤6
Optimization Equation: =2+5
z
=
2
x
+
5
y
Maximum Value of
z
:
Minimum Value of
z
:
Answer:
z(max) = 16
z(min) = -24
Step-by-step explanation:
2x - y = 12 multiply by 2
4x - 2y = 24 (1)
4x + 2y = 0 add equations
8x = 24
x = 3
4(3) + 2y = 0
y = -6
so (3, -6) is a common point on these two lines
z = 2(3) + 5(-6) = -24
4x - 2y = 24 (1)
x + 2y = 6 add equations
5x = 30
x = 6
6 + 2y = 6
y = 0
so (6, 0) is a common point on these two lines
z = 2(6) + 5(0) = 12
4x + 2y = 0 multiply by -1
-4x - 2y = 0
x + 2y = 6 add equations
-3x = 6
x = -2
-2 + 2y = 6
y = 4
so (-2, 4) is a common point on these two lines
z = 2(-2) + 5(4) = 16
7 days 8 hours 20 minutes
- 4 days 10 hours 30 minutes
2 days 21 hours
50 minutes
3 days 2 hours
10 minutes
7 days 8 hours
20 minutes
J 11 days 8 hours
50 minutes
K none of these
Answer:
A
Step-by-step explanation:
1 2 3
days hours minutes days hours minutes days hours minutes
7 8 20 6 24+8 20 6 31 60+20
4 10 30
-
_______________
4
days hours minutes
6 31 80
4 10 30
-
____________________
2 21 50
___________________
plz help I will give Brianly
A pair of linear equations is shown below: y = −x + 1 y = 2x + 4 Which of the following statements best explains the steps to solve the pair of equations graphically? (4 points) Select one: a. On a graph, plot the line y = −x + 1, which has y-intercept = −1 and slope = 1, and y = 2x + 4, which has y-intercept = 2 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution. b. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = 1, and y = 2x + 4, which has y-intercept = 1 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution. c. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = −2 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution. d. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.
Answer:
the answer is 89
Step-by-step explanation:
this is a hard one to salve but basically if you know and lern hout to do it it is not that hard
Solve.
x² + 5x – 2=0
Answer:
1
Use the quadratic formula
=
−
±
2
−
4
√
2
x=\frac{-{\color{#e8710a}{b}} \pm \sqrt{{\color{#e8710a}{b}}^{2}-4{\color{#c92786}{a}}{\color{#129eaf}{c}}}}{2{\color{#c92786}{a}}}
x=2a−b±b2−4ac
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
2
+
5
−
2
=
0
x^{2}+5x-2=0
x2+5x−2=0
=
1
a={\color{#c92786}{1}}
a=1
=
5
b={\color{#e8710a}{5}}
b=5
=
−
2
c={\color{#129eaf}{-2}}
c=−2
=
−
5
±
5
2
−
4
⋅
1
(
−
2
)
√
2
⋅
1
Step-by-step explanation:
this should help
Identify the X intercept and the yIntercept of the line 4x-2y=-12
Answer:
X-intercept = -3 and y-intercept = 6
Step-by-step explanation:
We can start off by isolating the y term. To do that, we must add 2y to both sides to get
[tex]4x=2y-12[/tex]
Now, we must add 12 to both sides and the y term will be all alone on the right side:
[tex]4x+12=2y[/tex]
Now, to have only y on the right side, we must divide by 2 to get:
[tex]y=2x+6[/tex]
In slope-intercept form, b is the y-intercept, and 'b' in this equation is 6. We have our y-intercept.
To find our x-intercept, y must be equal to zero. We can plug in that value for y and solve for x:
[tex]0=2x+6[/tex]
We can start off by subtracting 6 from both sides to get:
[tex]2x=-6[/tex]
We can then divide both sides to get [tex]x=-3[/tex] when y is equal to 0. Thus, we have our x-intercept.
Answer:
y-intercept= -6
x-intercept= 3
Step-by-step explanation:
First, rearrange the equation to be in y=mx+b.
4x-2y=12
4x-12=2y
(1/2)(4x-12)=y
y=2x-6
From here, we know that the 'b' in an equation in form y=mx+b is the y-intercept, which is -6.
To find the x intercept make y=0 and solve.
You can also solve without rearranging the equation and simply making x=0 and solving to find the y-intercept. and making y=0 and solving to find the x-intercept.
Find the value of each determinant
Answer:
−4304
Step-by-step explanation:
1. The given determinant is :
[tex]\begin{vmatrix}7 &31 \\ 142& 14\end{vmatrix}[/tex]
We need to find its determinant . It can be solved as follows :
[tex]\begin{vmatrix}7 &31 \\ 142& 14\end{vmatrix}=7(14)-142(31)\\\\=-4304[/tex]
So, the value of determinant is equal to −4304.
Answer:
A= -4269
B= 1768
C= 647.36
Step-by-step explanation:
What's the dependent variable shown in the table?
A)
The amount of water given to the plant
B)
The color of the flowers
C)
The number of flowers on the plant
D)
The speed at which the plant grows
Answer:
The number of flowers on the plant
Step-by-step explanation:
Answer:
C: Number of flowers on the plant
Step-by-step explanation:
i got it right on my test
The domain for all variables in the expressions below is the set of real numbers. Determine whether each statement is true or false.(i)∀x ∃y(x+y≥0)
The domain of a set is the possible input values the set can take.
It is true that the domain of ∀x ∃y(x+y≥0) is the set of real numbers
Given that: ∀x ∃y(x+y≥0)
Considering x+y ≥ 0, it means that the values of x + y are at least 0.
Make y the subject in x+y ≥ 0
So, we have:
[tex]\mathbf{y \le -x}[/tex]
There is no restriction as to the possible values of x.
This means that x can take any real number.
Hence, it is true that the domain of ∀x ∃y(x+y≥0) is the set of real numbers.
Read more about domain at:
https://brainly.com/question/15110684
Complete the remainder
Answer:
-14 is the answer for the second term (?)
Can anyone help with this math equation please?
Does the function ƒ(x) = (1∕2) + 25 represent exponential growth, decay, or neither?
A) Exponential growth
B) Impossible to determine with the information given.
C) Neither
D) Exponential decay
Answer:
A) Exponential growth
Step-by-step explanation:
You can work a total of no more than 35 hours each week at your two jobs. Housecleaning pays $7 per hour and your sales job pays $9 per hour. You need to earn at least $314 each week to pay your bills. Write a system of inequalities that shows the various numbers of hours you can work at each job.
Answer: 7x + 9y >_ (more or equal) 314
X + Y <_ ( less or equal) 35
Step-by-step explanation:
Answer:
h+s≤35 and 7h + 9s >_314
Step-by-step explanation:
[tex]\lim_{x\to \ 0} \frac{\sqrt{cos2x}-\sqrt[3]{cos3x} }{sinx^{2} }[/tex]
Answer:
[tex]\displaystyle \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \frac{1}{2}[/tex]
General Formulas and Concepts:
Calculus
Limits
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]
L'Hopital's Rule
Differentiation
DerivativesDerivative NotationBasic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
We are given the limit:
[tex]\displaystyle \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)}[/tex]
When we directly plug in x = 0, we see that we would have an indeterminate form:
[tex]\displaystyle \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \frac{0}{0}[/tex]
This tells us we need to use L'Hoptial's Rule. Let's differentiate the limit:
[tex]\displaystyle \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \displaystyle \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)}[/tex]
Plugging in x = 0 again, we would get:
[tex]\displaystyle \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)} = \frac{0}{0}[/tex]
Since we reached another indeterminate form, let's apply L'Hoptial's Rule again:
[tex]\displaystyle \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)} = \lim_{x \to 0} \frac{\frac{-[cos^2(2x) + 1]}{[cos(2x)]^{\frac{2}{3}}} + \frac{cos^2(3x) + 2}{[cos(3x)]^{\frac{5}{3}}}}{2cos(x^2) - 4x^2sin(x^2)}[/tex]
Substitute in x = 0 once more:
[tex]\displaystyle \lim_{x \to 0} \frac{\frac{-[cos^2(2x) + 1]}{[cos(2x)]^{\frac{2}{3}}} + \frac{cos^2(3x) + 2}{[cos(3x)]^{\frac{5}{3}}}}{2cos(x^2) - 4x^2sin(x^2)} = \frac{1}{2}[/tex]
And we have our final answer.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
what is symmetrical line
Answer:
assuming youre asking for line of symmetry, it's a line that cuts a shape exactly in half.
for example, a square has 4 lines of symmetry
Martha, Lee, Nancy, Paul, and Armando have all been invited to a dinner party. They arrive randomly, and each person arrives at a different time.
a. In how many ways can they arrive?
b. In how many ways can Martha arrive first and Armando last?
c. Find the probability that Martha will arrive first and Armando last.
Show your work
Answer:
a) 120
b) 6
c) 1/20
Step-by-step explanation:
a) 5! = 120
b) (5 - 2)! = 6
c) 6/120 = 1/20
what function represents exponential decay?
Answer:
There are two types of exponential functions: exponential growth and exponential decay. In the function f (x) = bx when b > 1, the function represents exponential growth. In the function f (x) = bx when 0 < b < 1, the function represents exponential decay.
Step-by-step explanation:
Find the lengths the missing side
Answer:
Short leg = x
Longer leg = 12
Hypotenuse = y
Short leg = 4√3
longer leg = 12
Hypotenuse = 8√3
Answered by GAUTHMATH
HELP PLEASE! I tried everything from adding to dividing, subtracting, multiplying but still no correct answer. Can someone help me out here please?
Answer:
46%
Step-by-step explanation:
Divde the smaller # by the bigger # to get the precentage
An average San Francisco customer uses what percent of electricity used by an average Houston customer?
In other words, San Francisco is what part of Houston?
---Just like, 7 is what part of 49? These are the same questions and would be solved in the same way
San Francisco / Houston
6753 / 14542
0.4644 = 46.44%
ANSWER: 46%
Hope this helps!
