Answer:
5 1/3 ÷ 2 2/3
Write both mixed fractions (whole number in front of fully-reduced fraction) as improper fractions (numerator is larger than denominator).
5 1/3 = 16/3
2 2/3 = 8/3
16/3 ÷ 8/3
When dividing, switch the numerator and the denominator of the fraction after the division sign and change the division sign to a multiplication sign.
16/3 x 3/8
Multiply.
16/8
Divide by 8.
2
Hope this helps! :)
in the figure above, the square ABCD is inscribed in a circle. if the radius of the circle is r, the hatbis the length of arc APD in terms of r?
a) (pi)r/4
b) (pi)r/2
c) (pi)r
d) (pi)r^2/4
The length of arc APD is: [tex]\frac{\pi r}{2}[/tex]
A square when inscribed in a circle will fit the circle such that, the 4 edges of the square touches the sides of the circle. The radius of the circle can be drawn from any of the 4 edges.
Given that ABCD is a square:
This means that:
[tex]AB = BC = CD = DA[/tex] --- equal side lengths
To calculate the length of arc APD, we make use of the following arc length formula
[tex]APD = \frac{\theta}{360} * 2\pi r[/tex]
Where
[tex]\theta = \angle ADO[/tex] and O is circle center
Since ABCD is a square, then:
[tex]\theta = \angle ADO = 90^o[/tex]
So, we have:
[tex]APD = \frac{90}{360} * 2\pi r[/tex]
[tex]APD = \frac{1}{4} * 2\pi r[/tex]
[tex]APD = \frac{\pi r}{2}[/tex]
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Points T, R, and P, define _____Points B, A, and E are:
Point A is located at (2, 4). Point B is located at (-2, 4). Point C is located at (-2, -4). Point D is located at (2, -4). Point E is located at (4, 4).
Answer:
Point T,R,P not seen how I don't understand your question.
Find the product and simplify your answer 6w(5w^2-5w+5)
If the product of a and cis negative, you subtract the factors of the product to arrive at c. True False
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Answer:
false
Step-by-step explanation:
The statement is nonsense (false). Regardless of the sign of a product, subtraction plays no part in anything related to it.
PPPPPLLLLZZZZ HELPPPP
Use the function f(x) = -16x² + 60x + 16 to answer the questions.
Part A: Completely factor f(x). (2 points)
Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points
Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph
Here we have the quadratic function:
f(x) = -16*x^2 + 60*x + 16
We can see that it is in standard form:
y = a*x^2 + b*x + c
a) First we want to completely factorize the function f(x).
To do it, we first need to find the roots of f(x).
Remember that for a generic quadratic equation:
a*x^2 + b*x + c = 0
whit roots x₁ and x₂, the factorized form is:
a*(x - x₁)*(x - x₂)
And the roots are given by:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4*a*c} }{2*a}[/tex]
Then for the case of f(x) = -16*x^2 + 60*x + 16, the roots are:
[tex]x = \frac{-60 \pm \sqrt{60^2 - 4*(-16)*16} }{2*(-16)} = \frac{-60 \pm 68}{-32}[/tex]
So the two roots are:
x₁ = (-60 + 68)/-32 = -0.25
x₂ = (-60 - 68)/-32 = 4
Then the factorized form is:
f(x) = -16*(x - 4)*(x + 0.25)
B) We already found the roots, which are:
x₁ = -0.25
x₂ = 4
These are the x-intercepts:
(-0.25, 0) and (4, 0)
C) We can see that the leading coefficient is negative.
This means that the arms of the graph go downwards, so as |x| increases, the value of f(x) tends to negative infinity.
D) To graph f(x) we can find some of the points of the graph (like the x-intercepts and some more of them) and then connect them with a parabola curve, the graph that you will get is the one that you can see below.
If you want to learn more about this topic, you can read:
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Find the remainder when f(x)=x3−4x2−6x−3 f ( x ) = x 3 − 4 x 2 − 6 x − 3 is divided by x+1
Answer:
The remainder is -2.
Step-by-step explanation:
According to the Polynomial Remainder Theorem, if we divide a polynomial P(x) by a binomial (x - a), then the remainder of the operation will be given by P(a).
Our polynomial is:
[tex]P(x) = x^3-4x^2-6x-3[/tex]
And we want to find the remainder when it's divided by the binomial:
[tex]x+1[/tex]
We can rewrite our divisor as (x - (-1)). Hence, a = -1.
Then by the PRT, the remainder will be:
[tex]\displaystyle\begin{aligned} R &= P(-1)\\ &=(-1)^3-4(-1)^2-6(-1)-3 \\ &= (-1)-4(1)+(6)-3 \\ &= -2 \end{aligned}[/tex]
The remainder is -2.
I NEED HELP ON C,E,F,G PLEASE ASAP!!!!
I need help answering this ASAP
Answer:
A the input x=3 goes to two different output values
Step-by-step explanation:
This is not a function
x = 3 goes to two different y values
x = 3 goes to t = 10 and y = 5
Given coordinates A(3,3),B(2,5),C(4,3) complete transformation. Complete double reflection over the lines y=2 followed by y=0.
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Answer:
A"(3, -1)B"(2, 1)C"(4, -1)Step-by-step explanation:
Reflection over 'a' then over 'b' will result in a translation of 2(b -a). Here, we have a=2, b=0, so the translation is 2(0-2) = -4. The reflection is over horizontal lines, so the transformation is ...
(x, y) ⇒ (x, y -4)
A(3, 3) ⇒ A"(3, -1)
B(2, 5) ⇒ B"(2, 1)
C(4,3) ⇒ C"(4, -1)
CAN SOMEBODY ANSWER MY QUESTIONS !!!!
9514 1404 393
Answer:
A''(-1, 2)B''(3, 5)C''(4, 3)Step-by-step explanation:
Reflection over the line x=a is the transformation ...
(x, y) ⇒ (2a -x, y)
Then the double reflection over x=a and x=b is the transformation ...
(x, y) ⇒ (2b -(2a -x), y) = (2(b-a) +x, y)
That is, the result is translation by twice the distance between the lines. For a=1 and b=3, the transformation is ...
(x, y) ⇒ (x +4, y) . . . . . . . translation to the right by 4 units.
A(-5, 2) ⇒ A''(-1, 2)
B(-1, 5) ⇒ B''(3, 5)
C(0, 3) ⇒ C''(4, 3)
question is in picture
Answer: A
Step-by-step explanation:
(tangent is opposite over adjacent)
[tex]tan(40)=\frac{x}{3.8}\\x=3.8*tan(40)[/tex]
A study was conducted to determine if there was a difference in the driving ability of students from West University and East University by sending a survey to a sample of 100 students at both universities. Of the 100 sampled from West University, 15 reported they were involved in a car accident within the past year. Of the 100 randomly sampled students from East University, 12 students reported they were involved in a car accident within the past year. True or False. The difference in driving abilities at the two universities is statistically significant at the .05 significance level.
Answer:
False
Step-by-step explanation:
Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
West University:
15 out of 100, so:
[tex]p_W = \frac{15}{100} = 0.15[/tex]
[tex]s_W = \sqrt{\frac{0.15*0.85}{100}} = 0.0357[/tex]
East University:
12 out of 100, so:
[tex]p_E = \frac{12}{100} = 0.12[/tex]
[tex]s_E = \sqrt{\frac{0.12*0.88}{100}} = 0.0325[/tex]
Test the difference in driving abilities at the two universities:
At the null hypothesis we test if there is no difference, that is, the subtraction of the proportions is 0, so:
[tex]H_0: p_W - p_E = 0[/tex]
At the alternative hypothesis, we test if there is a difference, that is, if the subtraction of the proportions is different of 0. So
[tex]H_1: p_W - p_E \neq 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the two samples:
[tex]X = p_W - p_E = 0.15 - 0.12 = 0.03[/tex]
[tex]s = \sqrt{s_W^2+s_E^2} = \sqrt{0.0357^2+0.0325^2} = 0.0483[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{0.03 - 0}{0.0483}[/tex]
[tex]z = 0.62[/tex]
P-value of the test and decision:
The p-value of the test is the probability that the proportions differ by at least 0.03, which is P(|z| > 0.62), that is, 2 multiplied by the p-value of z = -0.62.
Looking at the z-table, z = -0.62 has a p-value of 0.2676.
2*0.2676 = 0.5352.
The p-value of the test is 0.5352 > 0.05, which means that the difference in driving is not statistically significant at the .05 significance level, and thus the answer is False.
Can someone help me solve this and explain how to solve if possible please?
Teresita wanted to buy a dress for $50, but she decided to wait because she didn't have
enough money. A week later, the price had gone up 20%. Now she definitely had to wait to
buy it. A week later, she went back to the store, and the price had gone down 20% from the
last price. Teresita finally bought the dress. What did she pay for it?
Answer:
$48
Explanation:
> 50 x .20 = $10
$50 + $10= $60
-----------------------------
> 60 x .20 = $12
$60 - $12= $48
What is the value of b? -11b + 7 =40 (also there is another question in the bottom of the picture. If you can answer it please do)
Problem 1
The idea here is to follow PEMDAS in reverse to undo what is happening to the variable b, so we can isolate it.
-11b + 7 = 40
-11b = 40-7
-11b = 33
b = 33/(-11)
b = -3
To check this value, plug it back into the original equation. You should get 40 on each side to help confirm the answer.
Answer: b = -3=====================================================
Problem 2
There are two ways we can solve. One method is to use the hint your teacher gave you. So we'll distribute first and then follow the same idea as problem 1
9(p-4) = -18
9p-36 = -18
9p = -18+36
9p = 18
p = 18/9
p = 2
Another method you can use is to follow these steps
9(p-4) = -18
p-4 = -18/9
p-4 = -2
p = -2+4
p = 2
Either way, we get the same result. To check the answer, replace every p with 2 in the original equation. You should get -18 on the left side after simplifying.
Answer: p = 2At a time hours after taking a tablet, the rate at which a drug is being eliminated r(t)= 50 (e^-01t - e^-0.20t)is mg/hr. Assuming that all the drug is eventually eliminated, calculate the original dose.
Answer:
2500 mg
Step-by-step explanation:
Since r(t) is the rate at which the drug is being eliminated, we integrate r(t) with t from 0 to ∞ to find the original dose of drug, m. Since all of the drug will be eliminated at time t = ∞.
Since r(t) = 50 (e^-01t - e^-0.20t)
m = ∫₀⁰⁰50 (e^-01t - e^-0.20t)
= 50∫₀⁰⁰(e^-01t - e^-0.20t)
= 50[∫₀⁰⁰e^-01t - ∫₀⁰⁰e^-0.20t]
= 50([e^-01t/-0.01]₀⁰⁰ - [e^-0.20t/-0.02]₀⁰⁰)
= 50(1/-0.01[e^-01(∞) - e^-01(0)] - {1/-0.02[e^-0.02(∞) - e^-0.02(0)]})
= 50(1/-0.01[e^-(∞) - e^-(0)] - {1/-0.02[e^-(∞) - e^-(0)]})
= 50(1/-0.01[0 - 1] - {1/-0.02[0 - 1]})
= 50(1/-0.01[- 1] - {1/-0.02[- 1]})
= 50(1/0.01 - 1/0.02)
= 50(100 - 50)
= 50(50)
= 2500 mg
Move the numbers to the lines to order them from least to greatest.
least
greatest
67.98
68.6
68.11
Please answer ASAP
Answer:
67.98,68.11, 68.6
RATE OF CHANGE:
At the bakery shop, each baker works at his or her own speed, making the same
number of cakes each day. Marissa makes 28 cakes in 2 weeks, Carlos makes 60
cakes in 20 days, and Shelby makes 5 cakes in 2 days.
When the shop owner graphs the relationship between the number of cakes
made and days, who has the steepest graph? Explain.
Answer:
Carlos
Step-by-step explanation:
Hope this helps
Problem 2 find m<GEF
Answer:
m<GEF = 66°
Step-by-step explanation:
(72+60)/2
= 132/2
= 66
Answered by GAUTHMATH
What is the extreme value of the polynomial function f(x)= x2 - 4?
Answer:
+∞.
Step-by-step explanation:
That would be positive infinity.
The extreme value of the given polynomial [tex]f(x) = x^{2} -4[/tex] is ∞.
What is extreme value of a polynomial?Extreme values of a polynomial are the peaks and valleys of the polynomial—the points where direction changes.
What are the steps of finding the extreme value of any polynomial?The following steps which are required to find the extreme value of polynomial are:
Arrange the polynomial into the the form of [tex]ax^{2} +bs+c[/tex] where a, b and c are numbers.Determine whether a, the coefficient of the [tex]x^{2}[/tex] term, is positive or negative.If the term is positive, the extreme value will be the infinity because the value will continue to grow as x increases.If it is negative, use the formula [tex]\frac{-b}{2a}[/tex] to find the value for extreme. And then plug [tex]x = \frac{-b}{2a}[/tex] in the original polynomial to calculate the extreme value of the polynomial.According to the given question.
We have a polynomial
[tex]f(x) = x^{2} -4[/tex]
Since, in the given polynomial the coefficient of [tex]x^{2}[/tex] is positive . Therefore, the extreme value of the given polynomial is infinity because the value will continue to grow as x increases.
Hence, the extreme value of the given polynomial [tex]f(x) = x^{2} -4[/tex] is ∞.
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help. WORTH 15 POINTS!!!
Answer:
x=27
Step-by-step explanation:
The sum of the angles of a triangle are 180 degrees
90 + x+15 + 2x-6 = 180
Combine like terms
3x+99=180
Subtract 99 from each side
3x+99-99=180-99
3x =81
Divide each side by 3
3x/3 = 81/3
x=27
Which table represents a linear function
Answer:
3rd option (top right)
Step-by-step explanation:
3rd option represents a linear equation
y = -2x-1
Answered by GAUTHMATH
helppppp plsss ??? plssss ??
Answer:
3 is correct dear i hope it will help uFlying against the wind, an airplane travels 3360 kilometers in hours. Flying with the wind, the same plane travels 7560 kilometers in 9 hours. What is the rate of the plane in still air and what is the rate of the wind?
Answer:
606.6 and 233.3 respectively
Step-by-step explanation:
Let the speed of plane in still air be x and the speed of wind be y.
ATQ, (x+y)*9=7560 and (x-y)*9=3360. Solving it, we get x=606.6 and y=233.3
Use the distributive property to find the product of the rational number.
5/2 (- 8/5 + 7/5)
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Answer:
-1/2
Step-by-step explanation:
The factor outside parentheses multiplies each term inside.
5/2(-8/5 +7/5)
= (5/2)(-8/5) +(5/2)(7/5)
= -8/2 +7/2 = -1/2
Suppose a young sedentary woman wanted to lose 30 pounds of body fat in a period of 20 weeks. She now weighs 160 pounds and her activity level is such so she needs 15 Calories per pound of body weight to maintain her weight. Calculate the number of Calories she may consume daily in order to lose the 30 pounds by diet only. 1,000 1,250 1,400 1,650 1,900
Answer:
The answer is "1900"
Step-by-step explanation:
It takes 500 fewer calories per day for her to lose 1 lb of weight every week.
[tex]\to (15 \times 160)-500 =(2400)-500 =2400-500=1900[/tex]
What is the value of |-6|—|6|-(-6)?
The solution is
Answer:
6
Step-by-step explanation:
|-6| = 6
|6| = 6
- -6 = +6
so, we have
6 - 6 + 6 = 6
HELP ASAP PIC IS BELOW!!!
Answer:
55°
Step-by-step explanation:
Vertical angles are similar
Answered by GAUTHMATH
Choose the correct elements in the set for the following:
{y | y is an integer and y >/= -3}
{3, 4, 5, 6, . . .}
{−2, −1, 0, 2, . . .}
{−1, 0, 1, 2, . . }
{−3, −2, −1, 0, . . .}
****PLEASE explain your answer****
Answer:
D
Step-by-step explanation:
Y => - 3 that is {−3, −2, −1, 0, . . .}
Assume that human body temperatures are normally distributed with a mean of 98.19 and a standard deviation of 0.61
Answer:
Ok I'm assuming that know what??
Step-by-step explanation:
