Answer:
y = 1Step-by-step explanation:
Given the equation, 2x- y = 5, if x = 3, to get y we will simply substitute the value of x into the expression given as shown;
[tex]2x - y = 5\\\\Substituting \ x = 3\ into \ the \ equation\\\\2(3) - y = 5\\\\6 - y = 5\\\\subtracting\ 6\ from\ both\ sides\\\\6-6-y = 5- 6\\\\-y = -1\\\\multiplying\ both\ sides\ by \ -1\\-(-y) = -(-1)\\\\y = 1[/tex]
Hence, the value of y is 1
Jason has bought a new pool and has already measured some of the sides. Using the figure below and your knowledge of quadrilaterals, solve for x and y.
Answer:
x = 12
y = 12
Step-by-step explanation:
Each triangle is a right angle triangle
5² + x² = 13²
x² = 169 - 25
x = √144
x = 12
The shape is a parallelogram
Therefore
x = y
y = 12
find the value of x if (1.1)^x=100
Answer:
x ≈ 48.3177
Step-by-step explanation:
This is what logarithms are for (among other things).
log(1.1^x) = log(100)
x·log(1.1) = 2
x = 2/log(1.1) ≈ 48.3177
No clue how to graph this any help would be greatly appreciated
Answer:
First, you can graph the y-intercept. The y-intercept would be (0,3) or in your equation, the number 3. Next, you could create a table by substituting values for x such as 1, 2, 3, or 4. This will give you easy numbers to graph. Instead of creating a table, perhaps you want to graph this by plotting the slope. Since the slope is 3/2, is means that it is going up, because the number is positive. An easy way to start would be starting at your y-intercept, (0,3), you could go two to the right and three up. That is a point. Then you could go the way down; two to the left and three down. Finally, you can draw a line connecting the points together.
I hope this helped you! Have a great rest of your day!
Mario and tabitha are calculating the probability of getting a 4 and a 2 if they roll a die twice. Who is correct?
Answer:
[tex]\frac{2}{12}[/tex] simplified to [tex]\frac{1}{6}[/tex]
Step-by-step explanation:
4 = [tex]\frac{1}{12}[/tex]
2 = [tex]\frac{1}{12}[/tex]
[tex]\frac{1}{12}[/tex] + [tex]\frac{1}{12}[/tex] = [tex]\frac{2}{12}[/tex] ÷ 2 = [tex]\frac{1}{6}[/tex]
evaluate 25.1 * 2.51 in two decimal places
Answer:
63.00
Step-by-step explanation:
25.1 × 2.51
Multiply.
= 63.001
Round to two decimal places.
63.00
Answer:
63.00
Step-by-step explanation:
when u multiply 25.1 by 25.1 you get 630.01. Then u have to move the decimal over to the left once and then u get 63.00
what is u over 4-4= -20
u/4 - 4 = -20
Add 4 to both sides:
u/4 = -16
Multiply both sides by 4:
u = -64
Answer:
u=-64
Step-by-step explanation:
u/4 -4 = -20
First add 4 to both sides.
u/4=-16
Now multiply both sides by 4
u=-64
If nine of every 11 trick-or-treaters that came to your house last Halloween were dressed as pirates what proportion of trick-or-treaters were not dressed as pirates
Answer:
11 - 9 = 2 trick-or-treaters out of 11 were not dressed as pirates so the proportion is 2/11.
Answer: Ratio is 2:11
Step-by-step explanation:
So your ratio of pirates to non-pirates would be 9:11
So you subtract number of pirates from total trick-or-treaters and get 2.
So the proportion of non-pirates would be 2:11.
Grandpa and Grandma are treating their family to the movies. Matinee tickets cost $4 per child and $4 per adult. Evening tickets cost $6 per child and $8 per adult. They plan on spending no more than $80 on the matinee tickets and no more than $100 on the evening tickets.
Complete Question
Grandpa and Grandma are treating their family to the movies. Matinee tickets cost $4 per child and $4 per adult. Evening tickets cost $6 per child and $8 per adult. They plan on spending no more than $80 on the matinee tickets and no more than $100 on the evening tickets. Could they take 9 children and 4 adults to both shows? Show your work. A yes or no answer is not sufficient for credit.
Answer:
Yes it is possible to take the 9 children and 4 adults to both shows
Step-by-step explanation:
From the question we are told that
The cost of the Matinee tickets for a child is z = $4
The cost of the Matinee tickets for an adult is a = $ 4
The cost of the Evening tickets for a child is k = $6
The cost of the Evening tickets for an adult is b = $8
The maximum amount to be spent on Matinee tickets is m = $80
The maximum amount to be spent on Evening tickets is e = $100
The number of child to be taken to the movies is n = 9
The number of adults to be taken to the movies is j = 4
Now the total amount of money that would be spent on Matinee tickets is mathematically evaluated as
[tex]t = 4 n + 4 j[/tex]
substituting values
[tex]t = 4 * 9 + 4* 4[/tex]
[tex]t = 52[/tex]
Now the total amount of money that would be spent on Evening ticket is mathematically evaluated as
[tex]T = 6n + 8j[/tex]
substituting values
[tex]T = 6(9) + 8(4)[/tex]
[tex]T = 86[/tex]
This implies that it is possible to take 9 children and 4 adults to both shows
given that
[tex]t \le m[/tex]
i.e $56 [tex]\le[/tex]$ 80
and
[tex]T \le e[/tex]
i.e $ 86 [tex]\le[/tex] $ 100
An article gave the accompanying data on ultimate load (kN) for two different types of beams. Assuming the underlying distributions are Normal, calculate and interpret a 99% Cl for the difference between the true average load for the fiberglass beams and that for the carbon beams.
Type Sample size Sample Mean Sample SD
Fiberglass grid 26 33.4 2.2
Commercial carbon 26 42.8 4.3
grid
1. Calculate and interpret a 99% Cl for true average stance duration among elderly individuals.
2. Carry out a test of hypotheses at significance level 0.05 to decide whether true average stance duration is larger among elderly individuals than younger individuals.
Answer:
The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).
Step-by-step explanation:
We have to calculate a 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams.
The sample 1 (Fiberglass), of size n1=26 has a mean of 33.4 and a standard deviation of 2.2.
The sample 2 (Carbon), of size n2=26 has a mean of 42.8 and a standard deviation of 4.3.
The difference between sample means is Md=-9.4.
[tex]M_d=M_1-M_2=33.4-42.8=-9.4[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{2.2^2}{26}+\dfrac{4.3^2}{26}}\\\\\\s_{M_d}=\sqrt{0.186+0.711}=\sqrt{0.897}=0.9473[/tex]
The critical t-value for a 99% confidence interval is t=2.678.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_{M_d}=2.678 \cdot 0.9473=2.537[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M_d-t \cdot s_{M_d} = -9.4-2.537=-11.937\\\\UL=M_d+t \cdot s_{M_d} = -9.4+2.537=-6.863[/tex]
The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).
In this way, we can calculate the individual duration of each one and the duration time, knowing that the sample means:
The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is -11.937 and -6.863.
We have to calculate a 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams. The sample 1 (Fiberglass), of size n1=26 has a mean of 33.4 and a standard deviation of 2.2. The sample 2 (Carbon), of size n2=26 has a mean of 42.8 and a standard deviation of 4.3. The difference between sample means is Md=-9.4.
[tex]Sm_d= \sqrt{\frac{\sigma^2_1}{n_1} +\frac{\sigma^2_2}{n_2}} = \sqrt{(0.186)+(0.711) }= 0.9473[/tex]
The critical t-value for a 99% confidednce interval is t=2.678. The margin of error (MOE) can be calculated as:
[tex]MOE=t*8M_d = (2.678)(0.9473)= 2.537[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL= M_d-t*SM_d = -9.4-2.537= -11.937\\UL= M_d+t*SM_d= -9.4+2.537= -6.863[/tex]
The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).
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Which number is greatest? 6.23 times 10 Superscript 12 6.23 times 10 Superscript 8 6.23 times 10 Superscript negative 6 6.23 times 10 Superscript 3
The greatest number is 6.23 times 10 superscript 12.
How does scientific notations work?The number is written in the form [tex]a \times 10^b[/tex] where we have [tex]1 \leq a < 10[/tex]
The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).
We are given that the number so;
A.6.23 x 10^12 is equivalent to rolling the decimal 12 times to the right.
B.6.23 x 10^8 is equivalent to rolling the decimal 8 times to the right.
C.6.23 x 10^-6 is equivalent to rolling the decimal 6 times to the left.
D.6.23 x 10^3 is equivalent to rolling the decimal 3 times to the right.
This shows the 10 has been multiplied by itself thrice.
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Help please! Simplify 7/ √x
Answer:
[tex]\frac{7\sqrt{x} }{x}[/tex]
Step-by-step explanation:
To simplify 7/√x, we need to rationalize:
[tex]\frac{7}{\sqrt{x} } (\frac{\sqrt{x} }{\sqrt{x} } )[/tex]
When we multiply the 2, we should get our answer:
[tex]\frac{7\sqrt{x} }{x}[/tex]
Answer:
[tex]\frac{7\sqrt{x} }{x}[/tex]
Step-by-step explanation:
[tex]\frac{7}{\sqrt{x} } \\\\\frac{7}{\sqrt{x} } * \frac{\sqrt{x} }{\sqrt{x} } \\\\\frac{7\sqrt{x} }{\sqrt{x\sqrt{x} } } \\[/tex]
[tex]\frac{7\sqrt{x} }{x}[/tex]
Hope this helps! :)
4) A large number of people were polled and asked which of four different animals were their
favorite. 13% said Penguin, 21% said Iguana, 22% said Parrot, and 44% said Turtle. Suppose you
decide to carry out a simulation given these percentages. You decide to select two digits at a
time. Which would be a proper assignment of digits for these teams?
a) 01-13 = Penguin, 01-21 = Iguana, 01-22 = Parrot, 01-44 = Turtle
b) 00-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 = Turtle
c) 01-13 = Penguin, 14-35 = Iguana, 36-58 = Parrot, 59-99 & 00 = Turtle
d) 01-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 & 00 = Turtle
e) None of these
Answer:
d) 01-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 & 00 = Turtle
Step-by-step explanation:
13 − 01 + 1 = 13
34 − 14 + 1 = 21
56 − 35 + 1 = 22
99 − 57 + 1 + 1 = 44
Toby cuts a pizza into 6 equal slices. He eats half a slice. What fraction of the pizza has he eaten?
The pizza is cut into 6 slices so each slice would be 1/6 of the pizza.
He at 1/2 of a slice:
1/6 x 1/2 = 1/12 of the pizza
3a. Write an equation in slope-intercept form of a
line that passes through (2,1) and (6,-5).
Answer:
[tex]y = -3/2x + 4[/tex]
Step-by-step explanation:
[tex](2,1) and (6,-5).\\x_1 = 2\\x_2 = 6\\y_1 =1\\y_2 =-5\\\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1}\\ \\\frac{y-1}{x-2} = \frac{-5-1}{6-2}\\\\\frac{y-1}{x-2} = \frac{-6}{4} \\Cross-Multiply\\4(y-1) = -6(x-2)\\4y-4=-6x+12\\4y =-6x+12+4\\4y = -6x+16\\Divide through-by ; 4\\\frac{4y = -6x+16}{4} \\\\y = -\frac{3}{2} x +4[/tex]
Find the area of the yellow region.
Round to the nearest tenth.
15 cm
15 cm
Area = [ ? ] cm2
Answer:
48.3 cm²
Step-by-step explanation:
Let A be the area of the yellow region
A= the area of the square - the area of the quarter square
A= 15²-(15²*π)/4= 48.28≈ 48.3 cm²
Which of the following functions is graphed below?
Answer:
C
Step-by-step explanation:
C is the solution
Answer:
Option C
Step-by-step explanation:
The graph is a horizontal translation 4 units left and a vertical translation 2 units down ⇒ y= |x+4|-2
. A box contains four red, three yellow, and seven green balls. Three balls are randomly selected from the box without replacement. (a) What is the probability that all three balls are the same colo
Answer:
10/91
Step-by-step explanation:
Number of Red balls = 4
Number of Yellow balls = 3
Number of green balls=7
Total=4+3+7=14
If we pick three balls of the same color, there are three possibilities: (All Red, All Green Or all Yellow).
Therefore:
The probability that all three balls are the same color (note that the selections are without replacement)
=P(RRR)+P(GGG)+P(YYY)
[tex]=(\frac{4}{14} \times \frac{3}{13} \times \frac{2}{12})+(\frac{3}{14} \times \frac{2}{13} \times \frac{1}{12})+(\frac{7}{14} \times \frac{6}{13} \times \frac{5}{12})\\\\=\frac{1}{91} + \frac{1}{364}+ \frac{5}{52}\\\\=\frac{10}{91}[/tex]
The probability that all three balls are the same color is 10/91.
Using the following conversions between the metric and U.S. systems, convert the measurement. Round your answer to 6 decimal places as needed
1 meter ≈ 3.28 feet
1 Liter ≈ 0.26 gallons
1 kilogram ≈ 2.20 pounds
33.777 yd ≈ __________ km
Answer:
33.777 yd = 0.030886 km
Step-by-step explanation:
==>Given:
33.777 yd
==>Required:
Convert 33.777 yd to km to 6 decimal places, using the metric and U.S systems.
==>Solution:
To convert, note that 1 km = 1093.6133 yd.
Thus,
1 km = 1093.6133 yd
x km = 33.777 yd
Cross multiply
1 × 33.777 = 1093.6133 × x
33.777 = 1093.6133x
Divide both sides by 1093.6133, to solve for x
33.777/1093.6133 = x
0.03088569 = x
x ≈ 0.030886 (to 6 decimal places)
Therefore, 33.777 yd = 0.030886 km
What is the justification for step 2 in the solution process?
Answer:
Answer C
Step-by-step explanation:
You are balancing this equation out by subtracting 7x from both sides. This means you are using the subtraction property of equality.
Write a pair of integers whose sum is- -8
Answer:
-3+(-5)
Checking our answer:
Adding this does indeed give -8
Simply the expression 3.4-1/2(0.75)
Answer:
3.025
Step-by-step explanation:
3.4-1/2(0.75)
3.4-0.375
3.025
What is the value of X in equation? 1/3 X - 2/3 = - 18
Answer:
x=-52
Step-by-step explanation:
1/3x=-17 1/3
x=-52
2) Find the diameter.
4) If the diameter is equal to 3 inches ,d=
Answer:
d = 3 in
Step-by-step explanation:
Since we are trying to find the diameter, and the diameter is given to us as 3 in, our diameter is 3 in.
In 1998, as an advertising campaign, the Nabisco Company announced a "1000 Chips Challenge," claiming that every 18-ounce bag of their Chips Ahoy cookies contained at least 1000 chocolate chips. Dedicated statistics students at the Air Force Academy (no kidding) purchased some randomly selected bags of cookies and counted the chocolate chips. Some of their data are given below. 1219 1214 1087 1200 1419 1121 1325 1345 1244 1258 1356 1132 1191 1270 1295 1135 Find a 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies.
Answer:
A 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies is [1187.96, 1288.44].
Step-by-step explanation:
We are given that statistics students at the Air Force Academy (no kidding) purchased some randomly selected bags of cookies and counted the chocolate chips.
Some of their data are given below; 1219, 1214, 1087, 1200, 1419, 1121, 1325, 1345, 1244, 1258, 1356, 1132, 1191, 1270, 1295, 1135.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean number of chocolate chips = [tex]\frac{\sum X}{n}[/tex] = 1238.2
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex] = 94.3
n = sample of car drivers = 16
[tex]\mu[/tex] = population mean number of chips in a bag
Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-2.131 < [tex]t_1_5[/tex] < 2.131) = 0.95 {As the critical value of t at 15 degrees of
freedom are -2.131 & 2.131 with P = 2.5%}
P(-2.131 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.131) = 0.95
P( [tex]-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]1238.2-2.131 \times {\frac{94.3}{\sqrt{16} } }[/tex] , [tex]1238.2+2.131 \times {\frac{94.3}{\sqrt{16} } }[/tex] ]
= [1187.96, 1288.44]
Therefore, a 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies is [1187.96, 1288.44].
A very large batch of components has arrived at a distributor. The batch can be characterized as acceptable only if the proportion of defective components is at most .10. The distributor decides to randomly select 10 components and to accept the batch only if the number of defective components in the sample is at most 2. Let X denote the number of defective components in the sample. What is the distribution of X? Justify your answer.
Required:
What is the probability that the batch will be accepted when the actual proportion of defectives (p) is:_______
a, 0.01
b. 0.05
c. 0.10
d. 0.20
e. 0.25
Answer:
c. 0.10
Step-by-step explanation:
Hello!
To accept a batch of components, the proportion of defective components is at most 0.10.
X: Number of defective components in a sample of 10.
This variable has a binomial distribution with parameters n=10 and p= 0.10 (for this binomial experiment, the "success" is finding a defective component)
The distributor will accept the batch if at most two components are defective, symbolically:
P(X≤2)
Using the tables for the binomial distribution you can find the accumulated probability for a sample of n=10 with probability of success of p= 0.10 and number of successes x= 2
P(X≤2)= 0.9298
I hope this helps!
Dairy cows at large commercial farms often receive injections of bST (Bovine Somatotropin), a hormone used to spur milk production. Bauman et al. (Journal of Dairy Science, 1989) reported that 12 cows given bST produced an average of 28.0 kg/d of milk. Assume that the standart deviation of milk production is 2.25 kg/d.
Requried:
a. Find a 99% confidence interval for the true mean milk production.
b. If the farms want the confidence interval to be no wider than ± 1.25 kg/d, what level of confidence would they need to use?
Answer:
a) 26.33 kg/d and 29.67 kg/d
b) 94.5%
Step-by-step explanation:
a. Find a 99% confidence interval for the true mean milk production.
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.575*\frac{2.25}{\sqrt{12}} = 1.67[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 28 - 1.67 = 26.33 kg/d
The upper end of the interval is the sample mean added to M. So it is 28 + 1.67 = 29.67 kg/d
The 99% confidence interval for the true mean milk production is between 26.33 kg/d and 29.67 kg/d
b. If the farms want the confidence interval to be no wider than ± 1.25 kg/d, what level of confidence would they need to use?
We need to find z initially, when M = 1.25.
[tex]M = z*\frac{2.25}{\sqrt{12}} = 1.67[/tex]
[tex]1.25 = z*\frac{2.25}{\sqrt{12}} = 1.67[/tex]
[tex]2.25z = 1.25\sqrt{12}[/tex]
[tex]z = \frac{1.25\sqrt{12}}{2.25}[/tex]
[tex]z = 1.92[/tex]
When [tex]z = 1.92[/tex], it has a pvalue of 0.9725.
1 - 2*(1 - 0.9725) = 0.945
So we should use a confidence level of 94.5%.
Factor completely 5x(x + 3) + 6(x + 3). (1 point)
Answer:
The answer is ( 5x + 6 ) ( x + 3 )Step-by-step explanation:
5x(x + 3) + 6(x + 3)
The final answer is
( 5x + 6 ) ( x + 3 )
Hope this helps you
find the value of x that makes abcd a parallelogram
The 4 angles need to add to 360.
2 of them are 70
The other two need to equal 360-140 = 220
They are both the same so one angle needs to equal 220/2 = 110
Now find x:
X + 60 = 110
Subtract 60 from both sides:
X = 50. The answer is D
factorise 12x² + x - 20
━━━━━━━☆☆━━━━━━━
▹ Answer
(3x + 4) * (4x - 5)
▹ Step-by-Step Explanation
12x² + x - 20
Rewrite
12x² + 16x - 15x - 20
Factor out
4x(3x + 4) - 15x - 20
4x(3x + 4) - 5(3x + 4)
Factor
(3x + 4) * (4x - 5)
Hope this helps!
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what is 3 + 3 × 3 + 3 =
Answer:
15
Step-by-step explanation:
PEMDAS
3x3 = 9
3+3 = 6
9+6 = 15
By the BODMAS rule we get, 3 + 3 × 3 + 3 = 15
The acronym BODMAS rule is used to keep track of the right sequence of operations to do when solving mathematical issues. Brackets (B), order of powers or roots (O), division (D), multiplication (M), addition (A), and subtraction (S) are all represented by this acronym (S).
3 + 3 × 3 + 3 =
3 × 3 = 9
3 + 9 + 3 = 15.
Therefore, the correct answer is 15.
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