Answer:
[tex]x=2+\sqrt{11},\:x=2-\sqrt{11}[/tex]
Step-by-step explanation:
[tex]x^2-4x-7=0\\\mathrm{Solve\:with\:the\:quadratic\:formula}\\Quadratic\:Equation\:Formula\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\mathrm{For\:}\quad a=1,\:b=-4,\:c=-7:\quad x_{1,\:2}=\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}\\x=\frac{-\left(-4\right)+\sqrt{\left(-4\right)^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}:\quad 2+\sqrt{11}[/tex]
[tex]x=\frac{-\left(-4\right)-\sqrt{\left(-4\right)^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}:\quad 2-\sqrt{11}\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\x=2+\sqrt{11},\:x=2-\sqrt{11}[/tex]
Plz help me :(
Prove for any value of y the value of expression y^4−(y^2−9)(y^2+9) is divisible by 9.
PROOF:
[tex]y^4-(y^2-9)(y^2+9)\\=y^4 -(y^4-81)\\=y^4-y^4+81\\=81[/tex]
And 81 is ALWAYS divisible by 9
Answer:
Its 9*9
Step-by-step explanation:
The equation equals 81 and 9*9=81.
Have a great day! :)
Select the action you would use to solve x/3=12. Then select the property that justifies that action
Answer:
To solve this I would multiply both sides by 3
Step-by-step explanation:
i would use the multiplication property of equality
The property that justifies that action x/3=12 is a linear question using reciprocal law.
What is a linear equation?A linear equation has one or two variables.
No variable in a linear equation is raised to a power greater than 1.No variable is used as the denominator of a fraction. A linear equation is defined as an equation that is written in the form of ax+by=c. When solving the system of linear equations, we will get the values of the variable, which is called the solution of a linear equation.explanation:-
x/3= 12
x = 12*3 ( using reciprocal)
hence x = 36
solving this we will get the valve of Y if x is given.
Learn more about linear equations here:-https://brainly.com/question/14323743
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Suppose U.S. consumers 21 years and older consumed 26.4 gallons of beer and cider per person during 2017. A distributor in Milwaukee believes that beer and cider consumption are higher in that city. A sample of consumers 21 years and older in Milwaukee will be taken, and the sample mean 2017 beer and cider consumption will be used to test the following null and alternative hypotheses:
H0: μ ≤ 26.4
Ha: μ > 26.4
(a) Assume the sample data led to rejection of the null hypothesis. What would be your conclusion about consumption of beer and cider in Milwaukee?
a) Conclude that the population mean annual consumption of beer and cider in Milwaukee is greater than 26.4 gallons and hence lower than throughout the United States.
b) Conclude that the population mean annual consumption of beer and cider in Milwaukee is greater than 26.4 gallons and hence higher than throughout the United States.
c) Conclude that the population mean annual consumption of beer and cider in Milwaukee is less than or equal to 26.4 gallons and hence higher than throughout the United States.
d) Conclude that the population mean annual consumption of beer and cider in Milwaukee is less than or equal to 26.4 gallons and hence lower than throughout the United States.
(b) What is the Type I error in this situation? What are the consequences of making this error?
a) The type I error is rejecting H0 when it is true. This error would claim the consumption in Milwaukee is greater than 26.4 when it is actually less than or equal to 26.4.
b) The type I error is not rejecting H0 when it is true. This error would claim the consumption in Milwaukee is less than or equal to 26.4 when it is actually less than or equal to 26.4.
c) The type I error is not rejecting H0 when it is false. This error would claim the consumption in Milwaukee is less than or equal to 26.4 when it is actually greater than 26.4.
d) The type I error is rejecting H0 when it is false. This error would claim the consumption in Milwaukee is greater than 26.4 when it is actually greater than 26.4.
(c) What is the Type II error in this situation? What are the consequences of making this error?
a) The type II error is accepting H0 when it is true. This error would claim that the population mean annual consumption of beer and cider in Milwaukee is less than or equal to 26.4 gallons when it is less than or equal to 26.4.
b) The type II error is not accepting H0 when it is true. This error would claim that the population mean annual consumption of beer and cider in Milwaukee is greater than 26.4 gallons when it is not.
c) The type II error is accepting H0 when it is false. This error would claim that the population mean annual consumption of beer and cider in Milwaukee is less than or equal to 26.4 gallons when it is not.
d) The type II error is not accepting H0 when it is false. This error would claim that the population mean annual consumption of beer and cider in Milwaukee is greater than 26.4 gallons when it is greater than 26.4.
Answer:
Step-by-step explanation:
A. If the null hypothesis was rejected, the conclusion would be
b) Conclude that the population mean annual consumption of beer and cider in Milwaukee is greater than 26.4 gallons and hence higher than throughout the United States.
B. The correct option is
a) The type I error is rejecting H0 when it is true. This error would claim the consumption in Milwaukee is greater than 26.4 when it is actually less than or equal to 26.4.
C. The correct option is
c) The type II error is accepting H0 when it is false. This error would claim that the population mean annual consumption of beer and cider in Milwaukee is less than or equal to 26.4 gallons when it is not.
A certain city's population is 120,000 and decreases 1.4% per year for 15 years.
Is this exponential growth or decay? Growth
What is the rate of growth or decay?
What was the initial amount? 120000
What is the function?
What is the population after 10 years? Round to the nearest whole number.
Answer:
Decay Problem.Decay rate, r = 0.014Initial Amount =120,000[tex]P(t)=120000(0.986)^t[/tex]P(10)=104,220Step-by-step explanation:
The exponential function for growth/decay is given as:
[tex]P(t)=P_0(1 \pm r)^t, where:\\P_0$ is the Initial Population\\r is the growth/decay rate\\t is time[/tex]
In this problem:
The city's initial population is 120,000 and it decreases by 1.4% per year.
Since the population decreases, it is a Decay Problem.Decay rate, r=1.4% =0.014Initial Amount =120,000Therefore, the function is:
[tex]P(t)=120000(1 - 0.014)^t\\P(t)=120000(0.986)^t[/tex]
When t=10 years
[tex]P(10)=120000(0.986)^10\\=104219.8\\\approx 104220 $ (to the nearest whole number)[/tex]
question is attached
I apologize, I am stumped... I thought you would find either the centroid, circumcenter, or incenter of the triangle created but it didn't work quite right for me.
Which of the following is the solution to 4 | X+32 8 ?
A. XS-5 or x 2-1
B. X25 or x 2-1
C. $-5 and x-1
D. -1
SUBMIT
Answer:
A
Step-by-step explanation:
x + 3 must be 2 or greater, or -2 or less
So x must be ≥ -1 or ≤ -5
Please answer...i always answer... please
Answer:
A) -x + y = 2
B) x + 2y = 4
we add both equations
3 y = 6
y = 2
We put y = 2 into equation B)
x + 2 * 2 = 4
x = 0
***********************************************
A) -2x + y = 6
B) x + y = 0
We multiply B) by 2
B) 2 x + 2 y = 0 then we add A)
A) -2x + y = 6
3y = 6
y = 2
Therefore x = -2
Step-by-step explanation:
Increase £130 by 15%
Answer:
£149.5
Step-by-step explanation:
[tex]100 + 15 = 115\\115/100 = 1.15\\130 * 1.15 = 149.5[/tex]
Parker marks sixths on number line. He writes 5/6 just before 1. What fraction does he write on the first mark to the right of 1?
Answer: 7/6
Step-by-step explanation:
If he is writing sixths, then we have multiples of 1/6.
this is:
0*(1/6) = 0
1*(1/6) = 1/6
.
.
.
5*(1/6) = 5/6 (the numer he wrote at the left of 1)
6*(1/6) = 6/6 = 1
7*(1/6) = 7/6
So the number next to 1, (at the right of 1) must be 7/6.
You also can find it by adding 1/6 to 1.
1/6 + 1 = 1/6 + 6/6 = 7/6.
Answer:
[tex]7/6[/tex]
Explanation:
[tex]1/6 \approx 0.16666[/tex]
[tex]2/6 \approx 0.33333[/tex]
[tex]3/6 = 0.5[/tex]
[tex]4/6 \approx 0.66666[/tex]
[tex]5/6 \approx 0.83333[/tex]
[tex]6/6=1[/tex]
[tex]7/6 \approx 1.16666[/tex]
Please answer this correctly
Answer:
629
Step-by-step explanation:
l x w
25x14
4x7
12x18
5x7
629
Which is the value of this expression when a = negative 2 and b = negative 3? (StartFraction 3 a Superscript negative 3 Baseline b squared Over 2 a Superscript negative 1 Baseline b Superscript 0 Baseline EndFraction) squared
Answer:
27/8
Step-by-step explanation:
You seem to want to evaluate ...
[tex]\dfrac{3a^{-3}b^2}{2a^{-1}b^0}[/tex]
I like to simplify the expression first, even though the order of operations would have you evaluate it as is.
[tex]=\dfrac{3}{2}a^{-3-(-1)}b^{2-0}=\dfrac{3b^2}{2a^2}[/tex]
Substitute the given values for "a" and "b" and do the arithmetic.
[tex]=\dfrac{3(-3)^2}{2(-2)^2}=\dfrac{3\cdot 9}{2\cdot 4}=\boxed{\dfrac{27}{8}}[/tex]
The list of ordered pairs below represents a relation. {(−6,10),(−5,4),(−1,−9),(9,−4)} Find the range of the relation.
Answer:
The range is simply all the y values of the ordered pairs in the relation so the answer (in increasing order) is -9, -4, 4, 10.
the graph of f (x) shown below has the same shape as the graph of G (x) equals x ^ 4 but it is shifted 4 units to the right what is the equation
Answer:
D
Step-by-step explanation:
shifting 4 units to the right means that the new root = old root + 4
what that means is that the equation must have a transformation such that it equates to 0 with the root being 4 larger.
the root/vertex for x^4 is at x=0
we want the root to be at x=4
so that means we can subtract 4 from x
and get (x-4)^4
simplify : 3/5x+x , find the answer ?
Answer:
8x/5
There’s a 1 in front of the x also remember to always simplify
3/5x + 1x
Answer:8x/5
Step-by-step explanation:
A, B, and C are collinear points. B is between A and C. AB = 5x + 8 BC = 6x - 1 AC = 12x - 11 Find AC.
Answer:
AC = 198
Step-by-step explanation:
Since all these points are collinear, we know that the addition of AB plus BC should give the same as AC. We can then set an equation that addresses this identity:
AB + BC = AC
5x +8 +6x - 1 = 12x - 11
Now re-arranging like terms in order to combine them:
8 - 1 + 11 = 12x - 5x - 6x
19 - 1 = 12x - 11x
18 = x
Now that we know the value of 'x", we can determine the value of AC:
AC = 12x - 11
AC = 12 (18) - 11
AC = 216 - 18
AC = 198
A researcher conducts two studies on the effectiveness of a peer mentoring program. Self-evaluation ratings among participants before, during, and after the program were measured in both studies. In Study 1, 12 participants were observed, and in Study 2, 16 participants were observed. If Fobt = 3.42 in both studies, then in which study will the decision be to reject the null hypothesis at α= 0.05 level of significance?
Answer:
Study 2
Step-by-step explanation:
Okay, so in this question we are given the data or parameters or information Below;
=>" two studies were conducted on the effectiveness of a peer mentoring program."
=> "Self-evaluation ratings among participants before, during, and after the program were measured in both studies."
=> In Study 1, 12 participants were observed"
=> "Study 2, 16 participants were observed."
=> " If Fobt = 3.42 in both studies"
Say Vo = study 2 and V1 = study 1.
Hence, Vo: not effective.
V1 = effective.
The study in which the decision will be to reject the null hypothesis at α= 0.05 level of significance is the STUDY 2.
This is because the value of F > f-critical.
Jack has a rectangular patio with a length that is one foot less than twice its width. His neighbor Ron's patio has the same width but a length that is 5 feet more than its width. If Jack's patio is 120 square feet and Ron's patio is 104 square feet, how many square feet longer is Jack's patio than Ron's?
Answer:
difference in area = 16 ft²
if you use 8 the difference in length between Jack patio and his neighbor patio will be will be 15 - 13 = 2 ft
if you use 13 the difference i length will be 25 - 18 = 7 ft
Step-by-step explanation:
Jacks rectangular patio
width = a
length = 2a - 1
area = lw
where
l = length
w = width
area = 120 ft²
a(2a - 1)
2a² - a - 120 = 0
(a - 8) (2a + 15)
a = 8 or -15/2
Ron's rectangular patio
width = a
length = a + 5
area = lw
area = 104 ft²
a (a + 5) = 104
a² + 5a -104 = 0
(a + 8) (a - 13)
a = -8 or 13
How many square feet longer is jack patio longer than Ron's patio is the difference in their area. Therefore,
120 - 104 = 16 ft²
The value 8 or 13 can be used for a since the width a have to be the same.
if you use 8 the difference in length between Jack patio and his neighbor patio will be will be 15 - 13 = 2 ft
if you use 13 the difference i length will be 25 - 18 = 7 ft
:4. In the Department of Natural Sciences, 14 faculty members have a PhD, and 30 faculty members do not have a PhD. In the Department, the number of female faculty who do not have a PhD is 10 more than the number of females who have a PhD. If a third of the male faculty in the Department have a PhD, then what is the number of female faculty in the Department with a PhD?
Answer:
The number of female faculty in the Department with a PhD is 8.
Step-by-step explanation:
There are 14 + 30 = 44 faculty members.
Of those, x are male and y are female.
Then
x + y = 44.
The number of female faculty who do not have a PhD is 10 more than the number of females who have a PhD.
y = z + w
z is the number of females with PhD.
w is the number of females without PhD.
w = z + 10
If a third of the male faculty in the Department have a PhD
[tex]\frac{x}{3} + z = 14[/tex]
Now, we can write all variables as functions of z, which is the number of female faculty in the Department with PhD.
The objective is:
To find z from the first equation, that is:
[tex]x + y = 44[/tex]
To do this, we have to write x and y as functions of z.
Writing x and y as functions z.
[tex]\frac{x}{3} + z = 14[/tex]
[tex]\frac{x}{3} = 14 - x[/tex]
[tex]x = 3(14 - z)[/tex]
[tex]x = 42 - 3z[/tex]
And
[tex]y = z + w[/tex]
In which
[tex]w = 10 + z[/tex]
So
[tex]y = z + 10 + z[/tex]
[tex]y = 2z + 10[/tex]
Replacing:
[tex]x + y = 44[/tex]
[tex]42 - 3z + 2z + 10 = 44[/tex]
[tex]-z + 52 = 44[/tex]
[tex]z = 52 - 44[/tex]
[tex]z = 8[/tex]
The number of female faculty in the Department with a PhD is 8.
Select all fractions that are equal to 3/4
3/4, 6/8, 9/12, 12/16 , 15/20, 18/24, 21/28, 24/32 , 27/36, 30/40, 33/44, 36/48 , 39/52, 42/56, 45/60, 48/64 , 51/68, 54/72, 57/76, 60/80, ect..
I hope this is what you are looking for :)
Calculate the length of the apothem of a regular polygon. A
regular hexagon is shown. What is the length of the apothem,
rounded to the nearest inch? Recall that in a regular hexagon,
the length of the radius is equal to the length of each side of the
hexagon
10 in.
a
5 in
9 in
11 in
4 in
Answer:
9 in
Step-by-step explanation:
For an n-sided polygon, the length of the apothem is ...
a = r·cos(180°/n)
We assume your problem statement is saying the radius is 10 inches. For a hexagon, n=6 and we have ...
a = (10 in)cos(30°) ≈ 8.66 in
Rounded to the nearest inch, the apothem is 9 in.
build the greatest and the smallest number using the digit 7,2,6
greatest _____ and smallest ____
Factor 12q^2+34q-28. Include list of factors.
Answer:
2(2q+7)(3q-2)=0
Step-by-step explanation:
lets set up the equation equal to 0:
12q^2+34q-28=0
now, lets factor:
2(6q^2+17q-14)=0
2(2q+7)(3q-2)=0
now, lets find the solutions:
2q+7=0
2q=-7
q=-3.5
3q-2=0
3q=2
q=2/3
A 12cmx2cm rectangle sits inside a circle with a radius of 8cm. What isnthe area of the shaded region of the circle
Answer:
The answer would 177.06 centimeters
Please help me on this
Answer19/40=x/3.6
By cross multiplication
19*3.6=40*x
68.4 =40x
x=68.4/40
x=1.71
x=
Answer: C
Step-by-step explanation:
[tex]\frac{19}{40} = \frac{x}{3.6}[/tex] solve by cross product
40x = 68.4 Divide both sides by 40
x = 1.71
What are the terms in the algebraic expression
102 + 10 +
3b
Answer:
102, 10, and, 3b
Step-by-step explanation:
find the square root of 12 to the nearest hundredth
Answer:
\sqrt(12) hope this helped.
What’s the correct answer for this question ?
Answer:
C
Step-by-step explanation:
It closely resembles to a sphere.
simplify 8-(3a+8)=
havent done these in a while so...
Answer:
3
Step-by-step explanation:
8-(3a+8)
8-(11a)
8-11a
a=11-8
a=3
Answer:
0
Step-by-step explanation:
8-(3a+8)=0
8-3a-8=0
-3a=0
a=0
The loaves of rye bread distributed to a local store by a certain bakery have an average length of 30 centimeters and a standard deviation of 2 centimeters. Assuming the lengths are normally distributed. What percentage of loaves are between 26.94 and 32.18 centimeters
Answer:
79.91% of loaves are between 26.94 and 32.18 centimeters
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 30, \sigma = 2[/tex]
What percentage of loaves are between 26.94 and 32.18 centimeters
This is the pvalue of Z when X = 32.18 subtracted by the pvalue of Z when X = 26.94.
X = 32.18:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{32.18 - 30}{2}[/tex]
[tex]Z = 1.09[/tex]
[tex]Z = 1.09[/tex] has a pvalue of 0.8621
X = 26.94:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{26.94 - 30}{2}[/tex]
[tex]Z = -1.53[/tex]
[tex]Z = -1.53[/tex] has a pvalue of 0.0630
0.8621 - 0.0630 = 0.7991
79.91% of loaves are between 26.94 and 32.18 centimeters
A fire hydrant with a blue cap provides water at a rate of 1,500 gallons per minute. A fire hydrant with a green cap provides water at a rate of 1,000 gallons per minute. A fire hydrant with a purple cap provides water at half the rate of a fire hydrant with a green cap. What is the equation in fraction form
Answer:
Fire hydrant with a purple cap (with respect to a fire hydrant with a green cap):
[tex]\dot Q_{purple} = \frac{1}{2}\cdot \dot Q_{green}[/tex]
Step-by-step explanation:
The volume rate of the fire hidrant with a purple cap is equal to the product of the proportion factor and the volume rate of the fire hydrant with a concrete cap.
[tex]\dot Q_{i} = k \cdot \dot Q_{j}[/tex]
There are two different solutions:
Fire hydrant with a purple cap (with respect to a fire hydrant with a green cap):
[tex]\dot Q_{purple} = \frac{1}{2}\cdot \dot Q_{green}[/tex]
Fire hydrant with a purple cap (with respect to a fire hydrant with a blue cap):
[tex]\dot Q_{purple} = \frac{1}{2} \times \frac{1000\,gpm}{1500\,gpm}\cdot \dot Q_{blue}[/tex]
[tex]\dot Q_{purple} = \frac{1}{3}\cdot \dot Q_{blue}[/tex]
