[tex](x+3)(x+5)[/tex]
[tex]x(x+5)+3(x+5)[/tex]
[tex]x^2+5x+3x+15[/tex]
[tex]\displaystyle x^2+8x+15[/tex]
The volume of a water in a fish tank is 84,000cm the fish tank has the length 60cm and the width 35cm. The water comes to 10cm from the top of the tank. calculate the height of the tank.
Answer:
Height of tank = 50cm
Step-by-step explanation:
Volume of water from tank that the water is 10cm down is 84000cm³
Length = 60cm
Width = 35cm
Height of water = x
Volume = length* width* height
Volume= 84000cm³
84000 = 60*35*x
84000= 2100x
84000/2100= x
40 = x
Height of water= 40cm
Height of tank I = height of water+ 10cm
Height of tank= 40+10= 50cm
Height of tank = 50cm
Use Green's Theorem to evaluate ?C F·dr. (Check the orientation of the curve before applying the theorem.)
F(x, y) =< x + 4y3, 4x2 + y>
C consists of the arc of the curve y = sin x from (0, 0) to (p, 0) and the line segment from (p, 0) to (0, 0).
Answer:
Step-by-step explanation:
given a field of the form F = (P(x,y),Q(x,y) and a simple closed curve positively oriented, then
[tex]\int_{C} F \cdot dr = \int_A \frac{dQ}{dx} - \frac{dP}{dy} dA[/tex] where A is the area of the region enclosed by C.
In this case, by the description we can assume that C starts at (0,0). Then it goes the point (pi,0) on the path giben by y = sin(x) and then return to (0,0) along the straigth line that connects both points. Note that in this way, the interior the region enclosed by C is always on the right side of the point. This means that the curve is negatively oriented. Consider the path C' given by going from (0,0) to (pi,0) in a straight line and the going from (pi,0) to (0,0) over the curve y = sin(x). This path is positively oriented and we have that
[tex] \int_{C} F\cdot dr = - \int_{C'} F\cdot dr[/tex]
We use the green theorem applied to the path C'. Taking [tex] P = x+4y^3, Q = 4x^2+y[/tex] we get
[tex] \int_{C'} F\cdot dr = \int_{A} 8x-12y^2dA[/tex]
A is the region enclosed by the curves y =sin(x) and the x axis between the points (0,0) and (pi,0). So, we can describe this region as follows
[tex]0\leq x \leq \pi, 0\leq y \leq \sin(x)[/tex]
This gives use the integral
[tex] \int_{A} 8x-12y^2dA = \int_{0}^{\pi}\int_{0}^{\sin(x)} 8x-12y^2 dydx[/tex]
Integrating accordingly, we get that [tex]\int_{C'} F\cdot dr = 8\pi - \frac{16}{3}[/tex]
So
[tex] \int_{C} F cdot dr = - (8\pi - \frac{16}{3}) = \frac{16}{3} - 8\pi [/tex]
Keith Rollag (2007) noticed that coworkers evaluate and treat "new" employees differently from other staff members. He was interested in how long a new employee is considered "new" in an organization. He surveyed four organizations ranging in size from 34 to 89 employees. He found that the "new" employee status was mostly reserved for the 30% of employees in the organization with the lowest tenure.
A) In this study, what was the real range of employees hired by each organization surveyed?
B) What was the cumulative percent of "new" employees with the lowest tenure?
Answer:
a) Real range of employees hired by each organization surveyed = 56
b) The cumulative percent of "new" employees with the lowest tenure = 30%
Step-by-step explanation:
a) Note: To get the real range of employees hired by each organization, you would do a head count from 34 to 89 employees. This means that this can be done mathematically by finding the difference between 34 and 89 and add the 1 to ensure that "34" is included.
Real range of employees hired by each organization surveyed = (89 - 34) + 1
Real range of employees hired by each organization surveyed = 56
b) It is clearly stated in the question that the "new" employee status was mostly reserved for the 30% of employees in the organization with the lowest tenure.
Therefore, the cumulative percent of "new" employees with the lowest tenure = 30%
If the endpoints of AB have the coordinates A(9, 8) and B(-1, -2), what is the AB midpoint of ?
Answer:
(4, 3)
Step-by-step explanation:
Use the midpoint formula: [tex](\frac{x1+x2}{2}, \frac{y1+y2}{2} )[/tex]
The probability that a house in an urban area will be burglarized is 6%. If 10 houses are randomly selected, what is the probability that none of the houses will be burglarized?
Answer:
[tex](\dfrac{94}{100})^{10} \ or\ \approx 0.54[/tex]
Step-by-step explanation:
Given :
Probability that a house in an urban area will be burglarized,
[tex]p =6\%=\dfrac{6}{100}[/tex]
To find:
Probability that none of the houses randomly selected from 10 houses will be burglarized = ?
[tex]P(r=0) =?[/tex]
Solution:
This question is related to binomial distribution where:
[tex]p =\dfrac{6}{100}[/tex]
[tex]\Rightarrow[/tex] Probability that a house in an urban area will not be burglarized,
[tex]q =1-6\%=94\%=\dfrac{94}{100}[/tex]
Formula is:
[tex]P(r=x)=_nC_xp^xq^{n-x}[/tex]
Where n is the total number of elements in sample space and
x is the number selected from the sample space.
Here, x = 10 and
x = 0
[tex]\therefore P(r=0)=_nC_0p^0q^{10-0}\\\Rightarrow 1 \times (\dfrac{6}{100})^0\times (\dfrac{94}{100})^{10}\\\Rightarrow 1\times (\dfrac{94}{100})^{10}\\\Rightarrow (\dfrac{94}{100})^{10}\\\\\Rightarrow (0.94)^{10}\\\Rightarrow \approx 0.54[/tex]
For what values (cases) of the variables the expression does not exist: a / a−b
Answer:
a=b
Step-by-step explanation:
When the denominator is zero, the expression is undefined
a-b=0
a=b
The Speedmaster IV automobile gets an average of 22.0 miles per gallon in the city. The standard deviation is 3 miles per gallon. Find the probability that on any given day, the automobile will get less than 26 miles per gallon when driven in the city. Assume that the miles per gallon that this automobile gets is normally distributed.
Answer:
91% of the time the auto will get less than 26 mpg
Step-by-step explanation:
Think of (or draw) the standard normal curve. Mark the mean (22.0). Then one standard deviation above the mean would be 22.0 + 3.0, or 25.0. Two would be 22.0 + 2(3.0), or 28.0. Finallyl, draw a vertical line at 26.0.
Our task is to determine the area under the curve to the left of 26.0.
Using a basic calculator with built-in statistical functions, we find this area as follows:
normcdf(-100, 26.0, 22.0, 3.0) = 0.9088, which is the desired probability: 91% of the time the auto will get less than 26 mpg.
During the period of time that a local university takes phone-in registrations, calls come in at the rate of one every two minutes.a. What is the expected number of calls in one hour?b. What is the probability of three calls in five minutes?c. What is the probability of no calls in a five-minute period?
Answer:
Step-by-step explanation:
This is a poisson distribution. Let x be a random representing the number of calls in a given time interval.
a) the expected number of calls in one hour is the same as the mean score in 60 minutes. Thus,
Mean score = 60/2 = 30 calls
b) The interval of interest is 5 minutes.
µ = 5/2 = 2.5
We want to determine P(x = 3)
Using the Poisson probability calculator,
P(x = 3) = 0.21
c) µ = 5/2 = 2.5
We want to determine P(x = 0)
Using the Poisson probability calculator,
P(x = 0) = 0.08
1. A door of a lecture hall is in a parabolic shape. The door is 56 inches across at the bottom of the door and parallel to the floor and 32 inches high. Sketch and find the equation describing the shape of the door. If you are 22 inches tall, how far must you stand from the edge of the door to keep from hitting your head
Answer:
See below in bold.
Step-by-step explanation:
We can write the equation as
y = a(x - 28)(x + 28) as -28 and 28 ( +/- 1/2 * 56) are the zeros of the equation
y has coordinates (0, 32) at the top of the parabola so
32 = a(0 - 28)(0 + 28)
32 = a * (-28*28)
32 = -784 a
a = 32 / -784
a = -0.04082
So the equation is y = -0.04082(x - 28)(x + 28)
y = -0.04082x^2 + 32
The second part is found by first finding the value of x corresponding to y = 22
22 = -0.04082x^2 + 32
-0.04082x^2 = -10
x^2 = 245
x = 15.7 inches.
This is the distance from the centre of the door:
The distance from the edge = 28 - 15.7
= 12,3 inches.
Find the product of
3/5 × 7/11
Answer:
21/55
Step-by-step explanation:
Simply multiply the top 2 together:
3 x 7 = 21
And the bottom 2 together:
5 x 11 = 55
21/55 is your answer!
Let Aequals [Start 2 By 2 Matrix 1st Row 1st Column 3 2nd Column 2 2nd Row 1st Column negative 1 2nd Column 2 EndMatrix ]and Bequals [Start 2 By 2 Matrix 1st Row 1st Column 2 2nd Column 6 2nd Row 1st Column negative 3 2nd Column k EndMatrix ]. What value(s) of k, if any, will make ABequals BA?
Answer:
No value of k will make AB=BA
Step-by-step explanation:
[tex]A=\left(\begin{array}{ccc}3&2\\-1&2\end{array}\right), $ $B=\left(\begin{array}{ccc}2&6\\-3&k\end{array}\right) \\\\\\AB=\left(\begin{array}{ccc}3&2\\-1&2\end{array}\right)\left(\begin{array}{ccc}2&6\\-3&k\end{array}\right)=\left(\begin{array}{ccc}3*2+2*-3&3*6+2*k\\-1*2+2*-3&-1*6+2k\end{array}\right)=\left(\begin{array}{ccc}0&18+2k\\-8&-6+2k\end{array}\right)[/tex]
[tex]BA=\left(\begin{array}{ccc}2&6\\-3&k\end{array}\right)\left(\begin{array}{ccc}3&2\\-1&2\end{array}\right)=\left(\begin{array}{ccc}0&16\\-6&-6+2k\end{array}\right)[/tex]
We can see that [tex]AB \neq BA[/tex]. Therefore, there is no value of k that will make it equal. In general, matrix multiplication is not commutative.
Diego planted a 8 inch tall magical beanstalk. The height of the beanstalk increases by 16% each day.Write a function ff that determines the height of the beanstalk in inches in terms of the number of days tt since Diego planted the beanstalk f(t)=f(1)/f(0)=f(2)/f(1)=f(5.28)/f(4.28)=For any value of x, what is the value of f(x+1)/f(x)?
Answer:
The expression for the height of the plant is: f(x) = 8*(1.16)^x;
The value of f(x+1)/f(x) is 1.16.
Step-by-step explanation:
Since Diego's beanstalk grows at an exponential rate of 16% per day, then the expression that represents the height of the plant, "f", in function of days, "x", can be found as shown below:
Initially the height of the plant was:
[tex]f(0) = 8[/tex]
After the first day however it was:
f(1) = 8*(1 + \frac{16}{100}) = 8*(1.16)
While after the second day:
f(2) = f(1)*(1.16) = 8*(1.16)*(1.16) = 8*(1.16)²
And so on, therefore the expression is:
f(x) = 8*(1.16)^x
The value of f(x + 1)/f(x) is:
[8*(1.16)^(x + 1)]/[8*(1.16)^x]
[8*(1.16)*(1.16)^(x)]/[8*(1.16)^x] = 1.16
Sue works an average of 45 hours each week. She gets paid $10.12 per hour and time-and-a-half for all hours over 40 hours per week. What is her annual income?
Step-by-step explanation:
40 x $10.12/hr = $404.80
5 x $15.18/hr = $ 75.90
over time = $10.12 + $5.06 ( half of $10.12) = $15.18/hr
$404.80 + $75.90 = $480.70/weekly pay
assuming she works 52 weeks a year
$480.70 × 52 weeks = $24,996.40/yr
A College Alcohol Study has interviewed random samples of students at four-year colleges. In the most recent study, 494 of 1000 women reported drinking alcohol and 552 of 1000 men reported drinking alcohol. What is the 95% confidence interval of the drinking alcohol percentage difference between women and men
Answer:
The 95% confidence interval for the difference between the proportion of women who drink alcohol and the proportion of men who drink alcohol is (-0.102, -0.014) or (-10.2%, -1.4%).
Step-by-step explanation:
We want to calculate the bounds of a 95% confidence interval of the difference between proportions.
For a 95% CI, the critical value for z is z=1.96.
The sample 1 (women), of size n1=1000 has a proportion of p1=0.494.
[tex]p_1=X_1/n_1=494/1000=0.494[/tex]
The sample 2 (men), of size n2=1000 has a proportion of p2=0.552.
[tex]p_2=X_2/n_2=552/1000=0.552[/tex]
The difference between proportions is (p1-p2)=-0.058.
[tex]p_d=p_1-p_2=0.494-0.552=-0.058[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{494+552}{1000+1000}=\dfrac{1046}{2000}=0.523[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.523*0.477}{1000}+\dfrac{0.523*0.477}{1000}}\\\\\\s_{p1-p2}=\sqrt{0.000249+0.000249}=\sqrt{0.000499}=0.022[/tex]
Then, the margin of error is:
[tex]MOE=z \cdot s_{p1-p2}=1.96\cdot 0.022=0.0438[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=(p_1-p_2)-z\cdot s_{p1-p2} = -0.058-0.0438=-0.102\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= -0.058+0.0438=-0.014[/tex]
The 95% confidence interval for the difference between proportions is (-0.102, -0.014).
Point C ∈ AB and AB = 33 cm. Point C is 2 times farther from point B than point C is from point A. Find AC and CB.
Answer:
AC = 11 cm , CB = 22 cm
Step-by-step explanation:
let AC = x then BC = 2x , then
AC + BC = 33, that is
x + 2x = 33
3x = 33 ( divide both sides by 3 )
x = 11
Thus
AC = x = 11 cm and CB = 2x = 2 × 11 = 22 cm
Express the following ratio in it’s simplest form
5:20
Answer:
1:4
Step-by-step explanation:
Answer:
1 : 4
Step-by-step explanation:
5:20
Divide each side by 5
5/5 : 20/5
1 : 4
I WILL GIVE BRANLIEST!!! IT IS EXTREAMLY URGENT!!!! EASY I AM JUST DUMB
26. Jared visited his family doctor after suffering for days with a rash that appeared on his ankles and calves as soon as he arrived home from camp. Jared's doctor asked him several questions about his activities during the past week, including the places he'd been and the kind of clothing he wore. Then the doctor announced that Jared had a nasty case of poison ivy.
What kind of reasoning did Jared's physician use to make a diagnosis? Explain how you you were able to tell what kind of reasoning was used.
Answer:
Poison ivy rash is caused by contact with poison ivy, a plant that grows almost everywhere in the United States. The sap of the poison ivy plant, also known as Toxicodendron radicans, contains an oil called urushiol. This is the irritant that causes an allergic reaction and rash.
You don’t even have to come in direct contact with the plant to have a reaction. The oil can linger on your gardening equipment, golf clubs, or even your shoes. Brushing against the plant — or anything that’s touched it — can result in skin irritation, pain, and itching.
Jared might have told him about his activities similar to the ones like gardening etc. by which Jared's physician use to make a diagnosis.
He told doctor that he just returned from camp this clearly indicates that he might get in touch with plants .
Answer:
Deductive reasoning
Step-by-step explanation:
Deductive reasoning, he was given some simple information and any person could simply assume he had poison ivy, as it was made clear he had most likely been around it. And deductive reasoning is basically reasoning based off a few questions from which you can draw a conclusion from.
Suppose the solutions of a homogeneous system of four linear equations in five unknowns are all multiples of one nonzero solution. Will the system necessarily have have a solution for every possible choice of constants on the right sides of the equations? Explain.
Consider a homogeneous machine of four linear equations in five unknowns are all multiples of 1 non-0 solution. Objective is to give an explanation for the gadget have an answer for each viable preference of constants on the proper facets of the equations.
Yes, it's miles true.
Consider the machine as Ax = 0. in which A is 4x5 matrix.
From given dim Nul A=1. Since, the rank theorem states that
The dimensions of the column space and the row space of a mxn matrix A are equal. This not unusual size, the rank of matrix A, additionally equals the number of pivot positions in A and satisfies the equation
rank A+ dim NulA = n
dim NulA =n- rank A
Rank A = 5 - dim Nul A
Rank A = 4
Thus, the measurement of dim Col A = rank A = five
And since Col A is a subspace of R^4, Col A = R^4.
So, every vector b in R^4 also in Col A, and Ax = b, has an answer for all b. Hence, the structures have an answer for every viable preference of constants on the right aspects of the equations.
x + 7 = 6x - 3
answer plssss
Answer:
x=2
Step-by-step explanation:
x + 7 = 6x - 3
Subtract x from each side
x+7-x = 6x-x
7 = 5x-3
Add 3 to each side
7+3 = 5x-3+3
10 =5x
divide by 5
10/5 = 5x/5
2 =x
Answer:
x= 2
hope it helps!
Step-by-step explanation:
x + 7 = 6x - 3
Bring all the variables to one side
So get 6x to the other side
x+7-6x = -3
-5x +7 = -3
Take 7 to the other side
-5x= -3 -7
-5x = -3 + -7
-5x = -10
x = -10/-5
minus n minus becomes plus
x= 10/5
= 2
solve for x
2x/3 + 2 = 16
Answer:
2x/3 + 2= 16
=21
Step-by-step explanation:
Standard form:
2
3
x − 14 = 0
Factorization:
2
3 (x − 21) = 0
Solutions:
x = 42
2
= 21
Use the Factor Theorem to find ALL zeros of f(x) = x^3 - x^2 - 11x + 15, given that 3 is a zero. Show all work and express zeros in exact form (no decimals).
Answer:
Step-by-step explanation:
by synthetic division
3) 1 -1 -11 15
| 3 6 -15 (add)
____________
1 2 -5 |0
x²+2x-5=0
[tex]x=\frac{-2 \pm\sqrt{2^{2} -4*1*-5} }{2*1} \\or~x=\frac{-2 \pm\sqrt{4+20} }{2} \\or~x=\frac{-2 \pm2\sqrt{6} }{2} \\or ~x=-1 \pm \sqrt{6}[/tex]
what is 7/9 x 5 2/5 please!
Answer:
[tex]4\frac{1}{5}[/tex]
Step-by-step explanation:
=>[tex]\frac{7}{9} * 5 \frac{2}{5}[/tex]
=> [tex]\frac{7}{9} * \frac{27}{5}[/tex]
=> [tex]\frac{7*3}{5}[/tex]
=> [tex]\frac{21}{5}[/tex]
=> [tex]4\frac{1}{5}[/tex]
Answer:
[tex]4\frac{1}{5}[/tex]
Step-by-step explanation:
[tex]\frac{7}{9} \times 5 \frac{2}{5}[/tex]
[tex]\frac{7}{9} \times \frac{27}{5}[/tex]
[tex]\frac{7 \times 27}{9 \times 5 }[/tex]
[tex]\frac{189}{45}[/tex]
[tex]\frac{21}{5}[/tex]
[tex]=4\frac{1}{5}[/tex]
Suppose that prices of recently sold homes in one neighborhood have a mean of $225,000 with a standard deviation of $6700. Using Chebyshev's Theorem, what is the minimum percentage of recently sold homes with prices between $211,600 and $238,400
Answer:
[tex] 211600 = 225000 -k*6700[/tex]
[tex] k = \frac{225000-211600}{6700}= 2[/tex]
[tex] 238400 = 225000 +k*6700[/tex]
[tex] k = \frac{238400-225000}{6700}= 2[/tex]
So then the % expected would be:
[tex] 1- \frac{1}{2^2}= 1- 0.25 =0.75[/tex]
So then the answer would be 75%
Step-by-step explanation:
For this case we have the following info given:
[tex] \mu = 225000[/tex] represent the true mean
[tex]\sigma =6700[/tex] represent the true deviation
And for this case we want to find the minimum percentage of sold homes between $211,600 and $238,400.
From the chebysev theorem we know that we have [tex]1 -\frac{1}{k^2}[/tex] % of values within [tex]\mu \pm k\sigma[/tex] if we use this formula and the limit given we have:
[tex] 211600 = 225000 -k*6700[/tex]
[tex] k = \frac{225000-211600}{6700}= 2[/tex]
[tex] 238400 = 225000 +k*6700[/tex]
[tex] k = \frac{238400-225000}{6700}= 2[/tex]
So then the % expected would be:
[tex] 1- \frac{1}{2^2}= 1- 0.25 =0.75[/tex]
So then the answer would be 75%
Multi step equation 18=3(3x-6)
Answer: X= 4
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
18=3(3x−6)
18=(3)(3x)+(3)(−6)(Distribute)
18=9x+−18
18=9x−18
Step 2: Flip the equation.
9x−18=18
Step 3: Add 18 to both sides.
9x−18+18=18+18
9x=36
Step 4: Divide both sides by 9.
9x
9
=
36
9
Answer:
X=4
Step-by-step explanation:
18=3(3X-6)
18=3><(3X-6)
18=9X-18
9X=-18-18
9X=36
X=36/9
X=4
Hope this helps
Brainliest please
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
plane
Step-by-step explanation:
Answer:
D. Plane
Step-by-step explanation:
A plane extends in two dimensions. This figure is a plane. It is not a point, a segment or a ray.
Can someone plz help me solved this problem! I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!
Answer: $2 or $9
Step-by-step explanation:
Revenue (R) = $1800 , x = 1100 - 100p
R = xp
1800 = (1100 - 100p)p substituted x with 1100 - 100p
1800 = 1100p - 100p² distributed p into 1100 - 100p
100p² - 1100p + 1800 = 0 added 100p² & subtracted 1100p on both sides
p² - 11p + 18 = 0 divided both sides by 100
(p - 2) (p - 9) = 0 factored quadratic equation
p = 2 p = 9 applied Zero Product Property to solve for p
wo cards are selected from a standard deck of 52 playing cards. The first card is not replaced before the second card is selected. Find the probability of selecting a nine and then selecting an eight. The probability of selecting a nine and then selecting an eight is nothing.
Answer:
0.6%
Step-by-step explanation:
We have a standard deck of 52 playing cards, which is made up of 13 cards of each type (hearts, diamonds, spades, clubs)
Therefore there are one nine hearts, one nine diamonds, one nine spades and one nine clubs, that is to say that in total there are 4. Therefore the probability of drawing a nine is:
4/52
In the second card it is the same, an eight, that is, there are 4 eight cards, but there is already one less card in the whole deck, since it is not replaced, therefore the probability is:
4/51
So the final probability would be:
(4/52) * (4/51) = 0.006
Which means that the probability of the event is 0.6%
Which statement about perfect cubes is true?
Answer:
1. it has different colors
is 614 divisible by both 2 and 6?
Answer:
No
Step-by-step explanation:
It is not divisible by 6, for if you divide by 6, you will get a non natural number,
It is obviously divisible by 2.
So, No.
Answer:
no
Step-by-step explanation:
only by 2
614/2 = 307
614/6 = 102.33
The image of (6,9) under a dialation is (4,6). The scale factor is. -2, 2/3, or -2,3
Answer:
The scale factor is 2/3
Step-by-step explanation:
The image of (6,9) under a dilation is (4,6).
As you might see, there is a ratio between the image after dilating and before dilating, which is 4/6 = 6/9 = 2/3.
=> The scale factor is 2/3.