Answer:
a. 7k - 7
Step-by-step explanation:
Step 1: Write out expression
-k - (-8k + 7)
Step 2: Distribute negative
-k + 8k - 7
Step 3: Combine like terms
7k - 7
And we have our answer!
can you please help me with this
Answer:
[tex]\displaystyle A=\dfrac{1}{2}\int_\pi^{\frac{7\pi}{6}}{(\cos{\theta}+\sin{2\theta})^2}\,d\theta[/tex]
Step-by-step explanation:
The shaded area is the area of the curve bounded by θ = π and θ = 7π/6.* A differential of area in polar coordinates is ...
dA = (1/2)r^2·dθ
So, the shaded area is ...
[tex]\displaystyle\boxed{A=\dfrac{1}{2}\int_\pi^{\frac{7\pi}{6}}{(\cos{\theta}+\sin{2\theta})^2}\,d\theta}[/tex]
_____
* We found these bounds by trial and error using a graphing calculator to plot portions of the curve.
Please help with this
The shape has 11 sides.
Using the angle formula for polygons:
The sum of all the interior angles is:
11-2 x 180 = 9 x 180 = 1,620 degrees.
For one angle divide the total by number of sides:
1620 / 11 = 147.27 which rounds to 147.2
The answer is D.
Find the interquartile range of the data in the dot plot below. players blob:mo-extension://5f64da0e-f444-4fa8-b754-95
Answer:
[tex]IQR=Q_{3}-Q_{1}[/tex]
Step-by-step explanation:
The inter-quartile range is a measure of dispersion of a data set.
It is the difference between the third and the first quartile.
[tex]IQR=Q_{3}-Q_{1}[/tex]
The 1st quartile (Q₁) is well defined as the mid-value amid the minimum figure and the median of the data set. The 2nd quartile (Q₂) is the median of the data. The 3rd quartile (Q₃) is the mid-value amid the median and the maximum figure of the data set.
If In (x) = 3.53, what is the value of x ?
Find the rectangular coordinates of the point with the given polar coordinates.
Answer:
[tex]( - \sqrt{3} \: an d \: 1)[/tex]
In the following equation, when x=3, what is the value of y? -4x + 3y = 12 A. 9 B. 3 C. 0 D. 8 PLZ HURRY IM TIMED WILL MARK BRAINLIEST
Answer:
[tex]\huge\boxed{y = 8}[/tex]
Step-by-step explanation:
-4x + 3y = 12
Given that x = 3
-4 (3) + 3y = 12
-12 + 3y = 12
Adding 12 to both sides
3y = 12+12
3y = 24
Dividing both sides by 3
y = 8
Answer:
y =8
Step-by-step explanation:
-4x + 3y = 12
Let x = 3
-4(3) +3y = 12
-12+3y = 12
Add 12 to each side
-12+12+3y =12+12
3y =24
Divide each side by 3
3y/3 = 24/3
y =8
Shawna finds a study of American men that has an equation to predict weight (in pounds) from
height (in inches): y = -210 + 5.6x. Shawna's dad's height is 72 inches and he weighs 182 pounds.
What is the residual of weight and height for Shawna's dad?
a. 11.2 pounds
b. -11.2 pounds
c. 193.2 pounds
d. 809.2 pounds
Answer:
-11.2 pounds
Step-by-step explanation:
It is given that,
Shawna finds a study of American men that has an equation to predict weight (in pounds) from height (in inches):
y = -210 + 5.6x
Height of Shawna's dad is 72 inches
Weight is 182 pounds
We need to find the residual of weight and height for Shawna's dad.
Predicted weight of 72 inches men,
y' = -210 + 5.6(72)
y' = 193.2 pounds
So, residual is :
Y = 182 - 193.2
Y = -11.2 pounds
So, the residual of weight and height for Shawna's dad is -11.2 pounds.
Answer:
-11.2 pounds
Step-by-step explanation:
Got it right on the test.
the temperature at which water freezes on the celsius scale is 0 degrees C. It freezes at 32 degrees F on the Fahrenheit scale, write opposites fo these two numbers as integers.
Answer:
If we have an integer number N, the opposite of N will be:
-1*N = -N.
Then, the opposite of 0°C is:
-1*0°C = 0°C.
The number 0 is it's own opposite.
And for 32F, the opposite is:
-1*32F = -32F
So, while the numbers 0°C and 32F physically represent the same thing (the same temperature), mathematically, they behave differently.
A maker of microwave ovens advertises that no more than 10% of its microwaves need repair during the first 5 years of use. In a random sample of 50 microwaves that are 5 years old, 12% needed repairs at a=.04 can you reject the makers claim that no more than 10% of its microwaves need repair during the first five years of use?
Answer:
We conclude that no more than 10% of its microwaves need repair during the first five years of use.
Step-by-step explanation:
We are given that a maker of microwave ovens advertises that no more than 10% of its microwaves need repair during the first 5 years of use.
In a random sample of 50 microwaves that are 5 years old, 12% needed repairs.
Let p = population proportion of microwaves who need repair during the first five years of use.
So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 10% {means that no more than 10% of its microwaves need repair during the first five years of use}
Alternate Hypothesis, [tex]H_A[/tex] : p > 10% {means that more than 10% of its microwaves need repair during the first five years of use}
The test statistics that will be used here is One-sample z-test for proportions;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of microwaves who need repair during the first 5 years of use = 12%
n = sample of microwaves = 50
So, the test statistics = [tex]\frac{0.12-0.10}{\sqrt{\frac{0.10(1-0.10)}{50} } }[/tex]
= 0.471
The value of z-test statistics is 0.471.
Now, at a 0.04 level of significance, the z table gives a critical value of 1.751 for the right-tailed test.
Since the value of our test statistics is less than the critical value of z as 0.471 < 1.751, so we have insufficient evidence to reject our null hypothesis as the test statistics will not fall in the rejection region.
Therefore, we conclude that no more than 10% of its microwaves need repair during the first five years of use.
Cybil flips a coin and rolls a fair number cube at the same time. What is the probability that she will toss tails and roll a number less than 3? A. 1/6 B. 1/3 C. 2/5 D. 1/2 Please include ALL work! <3
[tex]|\Omega|=2\cdot6=12\\|A|=1\cdot2=2\\\\P(A)=\dfrac{2}{12}=\dfrac{1}{6}[/tex]
PLEASE FAST 40 POINTS
A box contains four tiles, numbered 1,4.5, and 8 as shown.
Kelly randomly chooses one tile, places it back in the box, then chooses a second tile.
What is the probability that the sum of the two chosen tiles is greater than 7?
A. 1/4
B. 5/16
C. 2/3
D. 11/16
Answer:
[tex]\bold{\dfrac{11}{16}}[/tex]
Step-by-step explanation:
Given four tiles with numbers:
1, 4, 5 and 8
Tile chosen once and then replaced, after that another tile chosen:
All possibilities are:
{(1, 1) ,(1, 4) ,(1, 5) ,(1, 8)
(4, 1) ,(4, 4) ,(4, 5) ,(4, 8)
(5, 1) ,(5, 4) ,(5, 5) ,(5, 8)
(8, 1) ,(8, 4) ,(8, 5) ,(8, 8) }
Total number of possibilities = 16
When the sum is greater than 7, the possibilities are:
{(1, 8)
(4, 4) ,(4, 5) ,(4, 8)
(5, 4) ,(5, 5) ,(5, 8)
(8, 1) ,(8, 4) ,(8, 5) ,(8, 8) }
Number of favorable cases = 11
Formula for probability of an event E is:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Hence, the required probability is:
[tex]\Rightarrow \bold{\dfrac{11}{16}}[/tex]
Answer:11/16
Step-by-step explanation:i took the test
Evaluating function expressions
-1•f(-8)-4•g(4)=
Answer: -7
Step-by-step explanation:
To find f(-8) look at the f function. Find the y value when x = -8
To find g(4) look at the g function. Find the y value when x = 3
Plug these values into the equation
-1 f(-8) - 4 f(4)
-1 (-5) - 4 (3)
5 - 12 = -7
Why would a linear function be an appropriate model?
Answer:
I know the answer
Step-by-step explanation:
Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.
60feet to meters plaese with work
Answer:
60 Feet = 18.288 Meters
Step-by-step explanation:
foot = 12 inch = 0.3048 m
0.3047 × 60
18.288 meters
The length of a rectangle is a inches. Its width is 5 inches less than the length. Find the area and the perimeter of the rectangle.
Answer:
[tex]Area = 5a - a^2[/tex] [tex]inches\²[/tex]
[tex]Perimeter = 10\ inches[/tex]
Step-by-step explanation:
Given
Length = a
Width = 5 - a
Required
Determine the Area and Perimeter;
Calculating Area
Area is calculated as thus;
[tex]Area = Length * Width[/tex]
Substitute values for Length and Width
[tex]Area = a * 5 - a[/tex]
[tex]Area = a * (5 - a)[/tex]
Open Bracket
[tex]Area = 5a - a^2[/tex]
Calculating Perimeter
Perimeter is calculated as thus;
[tex]Perimeter = 2 (Length + Width)[/tex]
Substitute values for Length and Width
[tex]Perimeter = 2 (a + 5 - a)[/tex]
Collect Like Terms
[tex]Perimeter = 2 (5 + a- a)[/tex]
[tex]Perimeter = 2 (5)[/tex]
Open Bracket
[tex]Perimeter = 10\ inches[/tex]
Consider the following. x = t2 − 2t, y = t5, 1 ≤ t ≤ 4 Set up an integral that represents the length of the curve. 4 1 dt Use your calculator to find the length correct to four decimal places.
Answer:
L ≈ 1023.0562
Step-by-step explanation:
We are given;
x = t² - 2t
dx/dt = 2t - 2
Also, y = t^(5)
dy/dt = 5t⁴
The arc length formula is;
L = (α,β)∫√[(dx/dt)² + (dy/dt)²]dt
Where α and β are the boundary points. Thus, applying this to our question, we have;
L = (1,4)∫√[(2t - 2)² + (5t⁴)²]dt
L = (1,4)∫√[4t² - 8t + 4 + 25t^(8)]dt
L = (1,4)∫√[25t^(8) + 4t² - 8t + 4]dt
Using online integral calculator, we have;
L ≈ 1023.0562
The length of the curve is 1023.0562 and this can be determined by doing the integration using the calculator.
Given :
[tex]\rm x = t^2-2t[/tex][tex]\rm y=t^5[/tex][tex]\rm 1\leq t\leq 4[/tex]First, differentiate x and y with respect to 't'.
[tex]\rm \dfrac{dx}{dt}=2t-2[/tex]
[tex]\rm \dfrac{dy}{dt}=5t^4[/tex]
Now, determine the length of the curve using the below formula:
[tex]\rm L = \int^b_a\sqrt{\left(\dfrac{dx}{dt}\right)^2+\left(\dfrac{dy}{dt}\right)^2} dt[/tex]
Now, substitute the value of the known terms in the above formula and then integrate it.
[tex]\rm L = \int^4_1\sqrt{(2t-2)^2+(5t^4)^2} dt[/tex]
[tex]\rm L = \int^4_1\sqrt{25t^8+4t^2-8t+4} \;dt[/tex]
Now, simplify the above integration using the calculator.
L = 1023.0562
For more information, refer to the link given below:
https://brainly.com/question/18651211
All human blood can be "ABO-typed" as O, A, B, or AB, but the distribution of the types varies a bit among groups of people. Here are the distributions of blood types for a randomly chosen person in China and in the United States:The probability O A B ABChinese 0.35 0.27 0.26 0.12American 0.45 0.4 0.11 0.04Suppose we randomly select an American and a Chinese, independently of each other, apply multiplication and addition probability rules, compute:a. Pr(They both have type O)b. Pr( they both have the same blood type)c. Pr( at least one person has type O)
Answer:
a. Pr(They both have type O)
= Pr(They both have type O)
= 0.35 x 0.45
= 0.1575 = 15.75%
b. Pr( they both have the same blood type)
= Pr( they both have the same blood type)
= 2/8
= 0.25 = 25%
c. Pr( at least one person has type O)
= Pr (at least one person has type O)
= 1 - 0.3575
= 0.6425 = 64.25%
Step-by-step explanation:
a) Data:
O A B AB
Chinese 0.35 0.27 0.26 0.12
American 0.45 0.4 0.11 0.04
b) Calculations:
i. Pr(They both have type O)
= Probability of Chinese with O multiplied by Probability of American with O
= 0.35 * 0.45
= 0.1575 = 15.75%
ii. Pr( they both have the same blood type)
= Probability of two out of 8 outcomes
= 2/8
= 0.25 = 25%
iii. Pr( at least one person has type O)
= Probability of (1 – p(none) )
The probability of none = p(none O blood type)
= p(none)
for Chinese = (0.27 + 0.26 + 0.12) * for American ( 0.4 + 0.11 + 0.04)
= 0.65 * 0.55 = 0.3575
Pr (at least one person has type O) = 1 - 0.3575
= 0.6425
Which values of x are point(s) of discontinuity for this function? Function x = –4 x = –2 x = 0 x = 2 x = 4
Answer:
x=0 and x=2
Step-by-step explanation:
We need to check at each point where the function changes definition
At x= -2
On the left side -4 on the right side = -( -2)^2 = -4 continuous
At x=0
The point is not defined since neither side has an equals sign
discontinuous
x =2
on the left side 2^2 =4 on the right side 2
It is discontinuous
Answer:
x = 0
x = 2
Step-by-step explanation:
Edge 2020
~theLocoCoco
Which is a perfect square? 6 Superscript 1 6 squared 6 cubed 6 Superscript 5 What is the length of the hypotenuse, x, if (20, 21, x) is a Pythagorean triple
Answer:
Step-by-step explanation:
Hello, by definition a perfect square can be written as [tex]a^2[/tex] where a in a positive integer.
So, to answer the first question, [tex]6^2[/tex] is a perfect square.
(a,b,c) is a Pythagorean triple means the following
[tex]a^2+b^2=c^2[/tex]
Here, it means that
[tex]x^2=20^2+21^2=841=29^2 \ \ \ so\\\\x=29[/tex]
Thank you.
Answer:
Its B
Step-by-step explanation:
Which equation is equivalent to StartRoot x EndRoot + 11 = 15?
Answer:
D [tex]\sqrt{x} +11=15[/tex]
Step-by-step explanation:
Edge 2020
For the given expression √x + 11 = 15 the value of x will be equal to 16.
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression √x + 11 =15. The expression will be solved as below,
√x + 11 =15
√x = 15 - 11
√x = 4
Squaring on both sides of the equation,
x = 4²
x = 16
To know more about an expression follow
https://brainly.com/question/25968875
#SPJ6
1.Write 32 1/2 in radical form
Answer:
√32
Step-by-step explanation:
Factor: 2(4-y)-j(4-y)
Answer:
(2-j)(4-y)
Step-by-step explanation:
Factoring using grouping,
(2-j)(4-y)
IM GIVING BRAINLIEST TO THE FIRST PERSON TO ANSWER!
Show ALL work please! <3
Answer:
B
Step-by-step explanation:
What work is there to show? you basically isolate x. add 2 to both sides. and you get x is greater than or equal to 5. So the answer is B.
x-2[tex]\geq[/tex]3
+2 +2
x[tex]\geq[/tex]5
A standardized exam's scores are normally distributed. In a recent year, the mean test score was and the standard deviation was . The test scores of four students selected at random are , , , and . Find the z-scores that correspond to each value and determine whether any of the values are unusual. The z-score for is nothing. (Round to two decimal places as needed.) The z-score for is nothing. (Round to two decimal places as needed.) The z-score for is nothing. (Round to two decimal places as needed.) The z-score for is nothing. (Round to two decimal places as needed.) Which values, if any, are unusual? Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The unusual value(s) is/are nothing. (Use a comma to separate answers as needed.) B. None of the values are unusual.
Answer:
The z-score for 1880 is 1.34.
The z-score for 1190 is -0.88.
The z-score for 2130 is 2.15.
The z-score for 1350 is -0.37.
And the z-score of 2130 is considered to be unusual.
Step-by-step explanation:
The complete question is: A standardized exam's scores are normally distributed. In recent years, the mean test score was 1464 and the standard deviation was 310. The test scores of four students selected at random are 1880, 1190, 2130, and 1350. Find the z-scores that correspond to each value and determine whether any of the values are unusual. The z-score for 1880 is nothing. (Round to two decimal places as needed.) The z-score for 1190 is nothing. (Round to two decimal places as needed.) The z-score for 2130 is nothing. (Round to two decimal places as needed.) The z-score for 1350 is nothing. (Round to two decimal places as needed.) Which values, if any, are unusual? Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The unusual value(s) is/are nothing. (Use a comma to separate answers as needed.) B. None of the values are unusual.
We are given that the mean test score was 1464 and the standard deviation was 310.
Let X = standardized exam's scores
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean test score = 1464
[tex]\sigma[/tex] = standard deviation = 310
S, X ~ Normal([tex]\mu=1464, \sigma^{2} = 310^{2}[/tex])
Now, the test scores of four students selected at random are 1880, 1190, 2130, and 1350.
So, the z-score of 1880 = [tex]\frac{X-\mu}{\sigma}[/tex]
= [tex]\frac{1880-1464}{310}[/tex] = 1.34
The z-score of 1190 = [tex]\frac{X-\mu}{\sigma}[/tex]
= [tex]\frac{1190-1464}{310}[/tex] = -0.88
The z-score of 2130 = [tex]\frac{X-\mu}{\sigma}[/tex]
= [tex]\frac{2130-1464}{310}[/tex] = 2.15
The z-score of 1350 = [tex]\frac{X-\mu}{\sigma}[/tex]
= [tex]\frac{1350-1464}{310}[/tex] = -0.37
Now, the values whose z-score is less than -1.96 or higher than 1.96 are considered to be unusual.
According to our z-scores, only the z-score of 2130 is considered to be unusual as all other z-scores lie within the range of -1.96 and 1.96.
Chelsea played her tuba from 4:25 pm until 5:07
Answer:
42 minutes
Step-by-step explanation:
if you are asking how long it takes Chelsea to play her tuba then you do: 67 - 25 = 42
Answer:
Step-by-step explanation:
jhngjnh
Find the area of the shaded regions:
area of Arc subtending [tex]360^{\circ}[/tex] (i.e. the whole circle) is $\pi r^2$
so area of Arc subtending $\theta^{\circ}$ is, $\frac{ \pi r^2}{360^{\circ}}\times \theta^{\circ}$
$\theta =72^{\circ}$ so the area enclosed by one such arc is $\frac{\pi (10)^272}{360}$
abd there are 2 such arcs, so double the area.
[tex] \LARGE{ \underline{ \boxed{ \rm{ \purple{Solution}}}}}[/tex]
Given:-Radius of the circle = 10 inchesAngle of each sector = 72°Number of sectors = 2To FinD:-Find the area of the shaded regions....?How to solve?For solving this question, Let's know how to find the area of a sector in a circle?
[tex] \large{ \boxed{ \rm{area \: of \: sector = \frac{\theta}{360} \times \pi {r}^{2} }}}[/tex]
Here, Θ is the angle of sector and r is the radius of the circle. So, let's solve this question.
Solution:-We have,
No. of sectors = 2Angle of sector = 72°By using formula,
⇛ Area of shaded region = 2 × Area of each sector
⇛ Area of shaded region = 2 × Θ/360° × πr²
⇛ Area of shaded region = 2 × 72°/360° × 22/7 × 10²
⇛ Area of shaded region = 2/5 × 100 × 22/7
⇛ Area of shaded region = 40 × 22/7
⇛ Area of shaded region = 880/7 inch. sq.
⇛ Area of shaded region = 125.71 inch. sq.
☄ Your Required answer is 125.71 inch. sq(approx.)
━━━━━━━━━━━━━━━━━━━━
Line k has a slope of 2/3. Find the slope of a line parallel to line k.
Answer:
We have to remember
slope = m
if the slope of line is parellel so it will be the same with other slope
m1= m2
2/3= 2/3
so the answer is 2/3
hope it helps ^°^
Answer:
2/3
Step-by-step explanation:
Parallel lines have the same slopes. Therefore,
[tex]m_{k} =m_{p}[/tex]
The slope of line k ([tex]m_{k}[/tex]) will be equal to the slope of the line parallel to k ([tex]m_{p}[/tex]).
We know that the slope of line k is 2/3.
[tex]m_{k}=\frac{2}{3}[/tex]
Therefore, the slope of the line parallel to line k is also 2/3.
[tex]\frac{2}{3}=m_{p}[/tex]
The slope of a line parallel to line k is 2/3.
y x1 x2
10 1 16
11 5 11
15 5 14
15 9 11
20 7 1
23 11 8
27 16 7
32 21 3
a. Using technology, construct a multiple regression model with the given data.
b. Interpret the meaning of the values for b1 and b2.
Answer:
ŷ = 0.964X1 - 0.336X2 + 13.066
b1 = 0.964 which is the unit change in the value of y when x1 changes.
b2 = - 0.336 which is the unit change in the value of y when x2 changes
Step-by-step explanation:
Y
10
11
15
15
20
23
27
32
X1
1
5
5
9
7
11
16
21
X2
16
11
14
11
1
8
7
3
The general form of a multiple regression equation is in form:
ŷ = b1x1 + b2x2 + c
Where,
ŷ = predicted or dependent variable
b1 and b2 = slope or gradient Coefficient for the independent or predictor variables x1 and X2 respectively.
c = intercept (constant)
Using the online multiple regression calculator, the model obtained by Inputting the values is written below:
ŷ = 0.964X1 - 0.336X2 + 13.066
Value of b1 = 0.964 which is the unit change in the value of y when x1 changes.
Value b2 = - 0.336 which is the unit change in the value of y when x2 changes
PLEASE HELP!!!
Evaluate the expression when b=4 and y= -3
-b+2y
Answer: -10
Step-by-step explanation: All you have to do is plug the values into the equation. -4+2(-3). Then you solve the equation using PEDMAS.
1. -4+2(-3)
2. -4+(-6)
3.-4-6
4.-10
Answer:
8
Step-by-step explanation:
-b + 2y
if
b = 4
and
y = 3
then:
-b + 2y = -4 + 2*6 = -4 + 12
= 8
A market survey shows that 50% of the population used Brand Z computers last year, 4% of the population quit their jobs last year, and 2% of the population used Brand Z computers and then quit their jobs. Are the events of using Brand Z computers and quitting your job independent
Answer:
the events of using Brand Z computers and quitting your job are independent.
Step-by-step explanation:
Let A be the event that the population used Brand Z computers and let B be the event that the population quit their jobs.
We are told that 50% of the population used Brand Z computers last year. Thus, the probability of event A is;
P(A) = 50% = 0.5
Also, we are told that 4% of the population quit their jobs last year. Thus the probability of event B is;
P(B) = 4% = 0.04
Since 2% of the population used Brand Z computers and then quit their jobs. Then the probability of the population used Brand Z computers and then quit their jobs is;
P(A ∩ B) = 2% = 0.02
From the law of independent events, if A and B are to be independent events, then;
P(A ∩ B) = P(A) × P(B)
Thus;
P(A ∩ B) = 0.5 × 0.04 = 0.02
This is same value as what was given in the question, thus the events of using Brand Z computers and quitting your job are independent.
