Given the equation: - 4 √x - 3 = 12
solve for x;
Divide both sides by -4 in [1]; we get;
√x - 3 = -3
Squaring both sides we get;
x -3 = (3)²
or
x - 3 = 9
Add 3 both sides we get;
x - 3 + 3 = 9 + 3
Simplify:
x= 12
Extraneous solution states that it is a root of a transformed equation that is not a root of the original equation because it was excluded from the domain of the original equation.
Substitute x= 12 in [1]
- 4√12 - 3 = 12
- 4√9 = 12
-4. 3 = 12
-12 = 12 False.
Therefore, the value of x is 12 and it is an extraneous solution.
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The school band collected $3,240 for 380 tickets sold to their spring concert. Adult tickets were $12 each and student tickets were $6 each. How many adult tickets were sold?
160 adult tickets were sold
How to determine how many adult tickets were sold?Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.
Set up equations to represent the problem.
Let the A and S represent the number of adult and student ticket respectively. So we can write:
12A + 6S = 3,240 --- (1)
A + S = 380 --- (2)
From (2):
S = 380 - A ---- (3)
Put (3) in (1):
12A + 6S = 3,240
12A + 6 (380 - A) = 3,240
12A + 2280 -6A = 3,240
6A = 3,240 - 2280
6A = 960
A = 960/6
A = 160 tickets
Thus, the number of adult ticket sold is 160
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What is the value of x
Answer:
54
Step-by-step explanation:
Find the indicated probability. In one town, 71% of adults have health insurance. What is the probability that 4 adults selected at random from the town all have health insurance
Answer:
0.254
Step-by-step explanation:
Given that:
Percentage of those having health insurance = 71%
p = 71 / 100 = 0.71
Number of adults selected at random, n = 4
Probability that 4 selected have health insurance :
p^n = 0.71^4 = 0.25411681
= 0.254
What is the surface area of the rectangular prism?
PLSSS HELP GUYS I NEED HELP ASAP
Answer:
348 ignore this eoendndisiwjd
Which expression is equivalent to 21^3sqrt15 - 9^3sqrt15?
A. 12
B. 30^3sqrt15
C. 12^3sqrt5
D. 12^3sqrt15
Answer:
the answer is D.
Step-by-step explanation:
Since the square: (3√15) is common in both of them, you only focus on 21 and 9. if you subtract 9 from 21, it will give you 12. so, just add (3√15) to 12, which will give you: 12^3sqrt15
Michelle is hosting a party that starts at 6:00 PM. She realizes she did not freeze the ice cubes! She puts ice cubes in the freezer at 1:00 PM hoping they freeze by the time the party starts. The water is 82 degrees Fahrenheit when put into the freezer and will freeze when it reaches 32 degrees Fahrenheit. In Michelle's freezer the water cools to 80% of the temperature from the previous hour. Will the ice cubes freeze before the party starts?
Answer:
2 hours?
Step-by-step explanation:
I put it in a calc
if we need to decrease the standard deviation of the sampling distribution by half what do we need to do to the sample size
Answer:
The answer is below
Step-by-step explanation:
For a normal distributed population with a mean (μ), and a standard deviation (σ), if a sample size of n is selected from the population, the mean of the sample ([tex]\mu_x[/tex]) = μ and the standard deviation of the sample ([tex]\sigma_x[/tex]) = [tex]\frac{\sigma }{\sqrt{n} }[/tex]
Let the normal distribution population have a standard deviation of σ. If the standard deviation is to be decreased by half, the sample size (n) needed is:
[tex]Using:\\\\\sigma_x=\frac{\sigma}{\sqrt{n} } \\\\but\ \sigma_x=\frac{\sigma}{2}\\\\Hence:\\\\ \frac{\sigma}{2}=\frac{\sigma}{\sqrt{n} }\\\\Divide\ through\ by \ \sigma\ to\ get:\\\\ \frac{1}{2}=\frac{1}{\sqrt{n} }\\\\\sqrt{n}=2\\\\square\ both\ sides:\\\\(\sqrt{n} )^2=2^2\\\\n=4\\\\[/tex]
To decrease the standard deviation of the sampling distribution by half we need a sample size of 4
Certain pieces made by an automatic lathe are subject to three kinds of defects X, Y, Z. A sample of 1000 pieces was inspected with the following results: 2.1% had type X defect. 24% had type Y defect. 2.8% had type Z defect. 0.3% had both type X and type Y defects. 04% had both type X and type Z defects. 0.6% had both type Y and type Z defects. 0.1% had type X, type Y, and type Z defects. Draw a Venn Diagram, then find:
(a) What percent had none of these defects?
(b) What percent had at least one of these defects?
(c) What percent were free of type X and/or type Y defects?
(d) What percent had not more than one of these defects?
Answer:
a) % age of samples containing none of these defects = 93.9%
b)% age of samples containing at least one of these defects = 6.1%
c) % age of samples free of type X and/or type Y defects = 95.8%
d) %age of samples with not more than 1 defect = 98.9%
Step-by-step explanation:
Data Given:
Number of Samples = 1000
Type X defect = 2.1% = 21 samples
Type Y defect = 2.4% = 24 samples
Type Z defect = 2.8% = 28 samples
Both Type X and Y defect = 0.3% = 3 samples
Both Type X and Z defect = 0.4% = 4 samples
Both Type Y and Z defect = 0.6% = 6 samples
Type X and Y and Z defect = 0.1% = 1 sample
Venn Diagram is attached in the attachment below. Please refer to attachment for the Venn Diagram.
a) % age of samples containing none of these defects.
Solution:
Number of samples containing none of these defects = Total - Samples with defects
Number of samples containing none of these defects = 1000 - { (Type X) + (Type Y) + (Type Z) - (Both X and Y) - (Both X and Z) - (Both Y and Z) + (All defects X and Y and Z) }
Number of samples containing none of these defects = 1000 - { (21) + (24) +(28) - (3) -(4) - (6) + (1) }
Number of samples containing none of these defects = 1000 - 61
Number of samples containing none of these defects = 939
% age of samples containing none of these defects = 939/1000 x 100
% age of samples containing none of these defects = 93.9%
b) % age of samples containing at least one of these defects:
We have already calculated this above, number of samples containing at least on of these defects:
number of samples containing at least on of these defects = { (Type X) + (Type Y) + (Type Z) - (Both X and Y) - (Both X and Z) - (Both Y and Z) + (All defects X and Y and Z) }
number of samples containing at least on of these defects = { (21) + (24) +(28) - (3) -(4) - (6) + (1) }
number of samples containing at least on of these defects = 61
% age of samples containing at least one of these defects = 61/1000 x 100
% age of samples containing at least one of these defects = 6.1%
c) % age of samples free of type X and/or type Y defects.
For this find, we need to find the samples with only Z Type defect.
Number of Samples with Only Z type defects = { (Type Z) - (Both X and Z) - (Both Y and Z) + (All defects X and Y and Z) }
Number of Samples with Only Z type defects = { (28) -(4) - (6) + (1) }
Number of Samples with Only Z type defects = 19
Now, we also know the number of samples without any defects = 939
Now,
The number of samples free of type X and/or type Y defect = Sum of Number of Samples with Only Z type defects and number of samples without any defects
The number of samples free of type X and/or type Y defect = 19+939
The number of samples free of type X and/or type Y defect = 958
% age of samples free of type X and/or type Y defects = 958/1000 x 100
% age of samples free of type X and/or type Y defects = 95.8%
d) %age of samples with not more than 1 defect:
For this find, we need to find number of samples with only X type and with only type Y and with only type Z.
We have already found the number of samples with only Z type defect = 19
Now,
number of samples with only X type defect = { (Type X) - (Both X and Z) - (Both X and Y) + (All defects X and Y and Z) }
number of samples with only X type defect = { (21) -(4) - (3) + (1) }
number of samples with only X type defect = 15
Similarly,
number of samples with only Y type defect = { (Type Y) - (Both Y and Z) - (Both X and Y) + (All defects X and Y and Z) }
number of samples with only Y type defect = { (24) -(6) - (3) + (1) }
number of samples with only Y type defect = 16
For,
samples with not more than 1 defect = number of samples with only Y type defect + number of samples with only X type defect + number of samples with only z type defect + number of samples without any defects
samples with not more than 1 defect = 939 + 16 + 15 + 19
samples with not more than 1 defect = 989
%age of samples with not more than 1 defect = 989/1000 x 100
%age of samples with not more than 1 defect = 98.9%
Each year, a school committee sells donated cakes to raise money for a trip. The table shows the number of cakes sold each year for 5 years.
Year 2011 2012 2013 2014 2015
Number of Cakes Sold 21 28 19 26 21
Which measure of center best summarizes the number of cakes sold each year, and what is the value of the chosen measure?
Move a word and a value to the lines to complete the sentences.
The best measure of center for this data is the
, which has a value of
mean
median
mode
21
22
23
Please help me
Answer:
MODE 21
Step-by-step explanation:
:)
Solve for t in terms of u, v, w, and x.
Answer:
there's no image lol
Step-by-step explanation
Meg is packing a shipping conditier.
There is one section of the shipping container that has not yet been packed. The space available is in the shape of rectangular
prism that measures 2 feet by 3 feet by 33 feet.
She will pack as many boxes into the available space as possible. Each box is in the shape of a cube with side length 1 foot.
The space available in the shinning container and one of the boxes are shown below.
Answer:
[tex]Boxes= 198[/tex]
Step-by-step explanation:
This question has uncleared details towards the end. However, one can deduce that we need to calculate the amount of box the available space can contain.
We have the following given parameters.
Shipping Container
[tex]Dimension: 2ft\ by\ 3ft\ by\ 33ft[/tex]
The box
[tex]Dimension: 1ft\ by\ 1ft\ by\ 1ft[/tex]
First, we calculate the volume of the shipping container.
[tex]V_A = 2ft * 3ft * 33ft[/tex]
[tex]V_A = 198ft^3[/tex]
Next, we calculate the volume of the box.
[tex]V_B = 1ft * 1ft * 1ft[/tex]
[tex]V_B = 1ft^3[/tex]
The number of box is then calculated as:
[tex]Boxes= \frac{V_A}{V_B}[/tex]
[tex]Boxes= \frac{198ft^3}{1ft^3}[/tex]
[tex]Boxes= \frac{198}{1}[/tex]
[tex]Boxes= 198[/tex]
Hence:
198 boxes will occupy the empty space
-1<9+n<17 and graph the answer after
Answer:
We get [tex]\mathbf{n>-10\:\:and\:\:n<8}[/tex]
Or we can write as: [tex]\mathbf{-10<n<8}[/tex]
The graph is shown is figure attached below:
Step-by-step explanation:
We need to solve the inequality [tex]-1<9+n<17[/tex] and graph the answer.
Solving the inequality
[tex]-1<9+n<17[/tex]
We know that if a<u<b then we can write a<u and u<b
So, we can write
[tex]-1<9+n \:and\: 9+n<17[/tex]
Solving these equations and finding values of n
[tex]-1<9+n \:and\: 9+n<17\\9+n>-1\:and\:9+n<17\\n>-1-9\:and\:n<17-9\\n>-10\:and\:n<8[/tex]
So, we get [tex]\mathbf{n>-10\:\:and\:\:n<8}[/tex]
We can write it as: -10< n and n<8
Overlapping we get: [tex]\mathbf{-10<n<8}[/tex]
The graph is shown is figure attached below:
Find the length of dm in the given fig.
Answer:
[tex]DM=12[/tex]
Step-by-step explanation:
(Let the point where the altitude from [tex]D[/tex] intersects [tex]AB[/tex] be called as point [tex]E[/tex].) First, let's find the area of parallelogram [tex]ABCD[/tex]. The area of a parallelogram is simply [tex]b*h=bh[/tex], where [tex]b[/tex] is the parallelogram's base and [tex]h[/tex] is the parallelogram's height. If we let [tex]AB[/tex] and [tex]DE[/tex] be the base and height respectively, since we are already given their lengths, we know that the area of parallelogram [tex]ABCD[/tex] will be [tex]AB*DE=15*8=120[/tex].
Now, how does this information matter, you might ask? Well, we can take either [tex]AB[/tex] or [tex]CB[/tex] to be the base and either [tex]DE[/tex] or [tex]DM[/tex] to be the height. In this case, let's take the latter two options, as we are looking to find the length of [tex]DM[/tex].
Therefore, we know that the area of parallelogram [tex]ABCD[/tex] can also be found by calculating [tex]CB*DM[/tex]. Since we know the values of the area and [tex]CB[/tex], we can write the following equation to solve for [tex]DM[/tex]:
[tex]Area = CB*DM[/tex]
[tex]120=10*DM[/tex] (Substitute [tex]Area=120[/tex] and [tex]CB=10[/tex] into the equation)
[tex]\frac{120}{10}=\frac{10*DM}{10}[/tex] (Divide both sides of the equation by [tex]10[/tex] to get rid of [tex]DM[/tex]'s coefficient)
[tex]12=DM[/tex] (Simplify)
[tex]DM=12[/tex] (Symmetric Property of Equality)
Hope this helps!
Please please help
Find the measure of the missing angle.
63°
Answer:
27 degrees
Step-by-step explanation:
Answer:
a = 27° ______
Step-by-step explanation:
~~~~~~~~~~
Determine the value of x in the equation below.
x/5 =15
Answer:
2
Step-by-step explanation:
Consider the series 7/9+7/27+7/81+7/243
Answer:
=1 37/243
Step-by-step explanation:
the series is that the numerator is all 7
srry if its wrong i dont rlly understand what its asking
Answer:
= 1.1522....
Step-by-step explanation:
7/9 +7/27 +7/81 + 7/243
189 + 63 + 1,701 + 567
243. 19,683
= 252 + 2,268
243. 19,683
= 4,960,116 + 551,124
4,782,969
= 5,511,240
4,782,969
= 1.15
Find the percent change from the first value to the second.
60; 90
Answer:
Step-by-step explanation:
90 is half again as much as 60: 60 + (1/2)(60) = 90
This is a 150% increase.
what a ratio of 4 days to 36 hours
Answer:
4:36
24 x 4:36
96:36
8:4
1day = 24 hours
Step-by-step explanation:
please help and can someone explain what a integer is
w = -18
x = -10
y = -2
z = 10
x and z are opposite, x= -10, where as z = 10, Hence x times (-1) equals z.
An integer is a non-fractional number real number. It can be either negative or positive, it simply cannot be a fraction.
"w", "x", and "y" are negative, and hence less than zero.
PLEASE HELP IM GIVING OUT BRAINLIEST (30 POINTS)
Answer:
1.) ax2+Bx+c
2.) parabola
3.) I don't know
4.) I don't know
5.) maximum
6.) minimum
7/8) The solutions of a quadratic equation are also called roots, zeroes, and x -intercepts.
I hope this kinda helped.
Answer:
1.) ax2+Bx+c
2.) parabola
3.) I don't know
4.) I don't know
5.) maximum
6.) minimum
7/8) The solutions of a quadratic equation are also called roots, zeroes, and x -intercepts.
I hope this kinda helped.
The letters from the word MATHEMATICS are placed in a hat. What is the probability of selecting an M and then selecting a T if the letters are selected at random and not replaced?
Please solve this. 10 points.
Answer:
Step-by-step explanation:
14x5-22
Please help! It due in a couple of minutes and I completely forgot how to do this.
There are 5 red marbles, 6 blue marbles, 3 green marbles, 4 black marbles, and 2 yellow marbles in a bag. A marble will be drawn from the bag and replaced 100 times. What is the reasonable prediction for the number of times a green or black marble will be drawn? A:14 B:65 C:7 D:35
Answer:
Here
Step-by-step explanation:
Make each one fraction like 5 red will be a 1/20 chance. After you make them all fractions, multiply the right ones(green or black).
What is the binomial expansion of (2x – 3)5?
Determine whether m(t)=(4/5)^t represents exponential growth or exponential decay. And Identify the percent rate of change.
Answer:
Step-by-step explanation:
exponential decay
rate of change: 20%
Four points are always coplanar if they:
Four points are always coplanar if they: lie in same plane.
Firstly understanding the coplanar points. Coplanar points are refers to the points if they are present in same plane. Further defining the word "plane". Plane is the surface, which is flat and two dimensional in nature. The surface is infinite. Plane can also be referred as the analogue of 3 dimensional space, you we can also interpret the plane as extension of point or line.
So, the points that lie on different planes will not be coplanar. Now, understanding the points on lines. Two or more lines may or may not be in same plane. Subsequently, points may or may not be coplanar, depending upon the lines they are placed on. Thus, we can not definitely say that points lying on the same line are coplanar.
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Analysis of variance is used to ______. A. simultaneously compare several population means B. compute a t test C. compare nominal data D. compare population proportions
Answer:
"Option A" is the right alternative.
Step-by-step explanation:
ANOVA could also be utilized to predict the dependent variable of even more with around 2 categories and seems to be compared to the general population extra influential throughout this circumstance. Throughout addition, ANOVA variants typically include covariates that encourage somebody to manipulate numerically for confounding factors as well as to recognize interactions wherein the factor progressives the implications of some other factor.Other provided preferences weren’t comparable to the same circumstances in question.
y=$1.25x + $5.00 what is the total cost of service for the month if you stream 5 videos
Answer: $11.25
Step-by-step explanation:
Answer:
$11.25
Step-by-step explanation:
I assume that x = the 5 videos streamed
5*1.25=6.25
6.25+5 =11.25
y=$11.25
2+4x=2(2x+1)
Which statements are true?
Select each correct answer.
There is no value for x that will make the equation true.
The equation is an identity,
The solution is 2.
There are infinitely many solutions.
The equation is a contradiction.
There are no solutions.
The equation is true for all values of x.
15% of the skittles in andys bag are green. how many skittles are in the bag if 9 of them are green
Answer:
60
Step-by-step explanation:
9/15=0.6
0.6x100=60