The y-intercept is 3.78.
We have given that,
[tex]\overline{x}=7.8 ,S_x=3.70,\\\overline{y}= 12.2,S_y=4.15\\r=0.964[/tex]
What is the formula of the slope?[tex]Slope=r \times\frac{S_y}{S_x} \\\\Slope=0.964\times \frac{4.15}{3.70}\\ Slope=1.08=\overline{y}-slope\:\times \overline{x}\ intercept\\=\overline{y}-slope\:\times \overline{x}\\=12.2-1.08(7.8)\\=3.78[/tex]
Therefore the y-intercept is 3.78.
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A factory that manufactures bolts is performing a quality control experiment. Each object should have a length of no more than 15 centimeters. The factory believes that the length of the bolts exceeds this value and measures the length of 75 bolts. The sample mean bolt length was 15.07 centimeters. The population standard deviation is known to be a = 0.26 centimeters. What is the test statistic z? Ex: 1.23 What is the p-value? Ex. 0.123 Does sufficient evidence exist that the length of bolts is actually greater than the mean value at a significance level of a 0.01?
The test statistic z is 2.33, the p-value corresponding to the test statistic z value is 0.0099.
What is Probability?Probability is the measure of the likeliness of happening of an event.
The mean of the data is 15.07 centimeters
The standard deviation of the data is 0.26 centimeters.
n = 75
Significance Level ∝ = 0.01
According to the null and alternative hypothesis
Hₐ : [tex]\rm \mu[/tex] ≤15 vs H₁ : [tex]\rm \mu[/tex] >15
The test statistic z is given by
[tex]\rm Z = \dfrac{(X-\mu)}{\sigma/\sqrt{n}}[/tex]
Z = ( 15.07 -15)/(0.26/√75)
Z = 2.33
The p-value corresponding to z value is 0.0099
as p-value < significance level, therefore the H₁ : [tex]\rm \mu[/tex] >15 is acceptable.
No, significant evidence is not present to tell that the length of bolts is actually greater than the mean value at a significance level of 0.01.
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If x dozen eggs cost y dollars, what is the cost, C, of z dozen eggs?
Answer:
c=y×z
Step-by-step explanation:
the answer is this because z would be the number of dozens you have times y the cost of one by multiplying those together you will get the cost of the z dozens of eggs
Please help!! Having a hard time with this! Bob can buy individual songs for $1.00 to download, or an entire album costs $10.00 to download. He can spend no more than a total of $60. He wants to buy at least three albums, and no more than 35 individual songs.
The following system of inequalities represents this situation, where x is the number of individual songs and y is the number of albums.
x + 10y ≤ 60
x ≤ 35
y ≥ 3
Which yellow shaded region corresponds to Bob’s possible choices?
Answer:
second one listed
Step-by-step explanation:
second one given--he can buy between 3 and 6 albums; and 0 to 30 songs
(if he were to buy exactly 3 albums, he could not buy more than 30 songs; which is why that portion of the graph is not shaded)
(shaded = possible)
hope this helps!
Which measures are true for the quilt piece? select three options. a = 60° x = 3 in. the perimeter of the rhombus is 16 inches. the measure of the greater interior angle of the rhombus is 90°. the length of the longer diagonal is approximately 7 inches.
The measures that are true for the quilt piece include:
a=. = 60°The perimeter of the rhombus is 16 inches.The length of the longer diagonal is 7 inches.How to depict the information?The value of a will be:
= 90° - 30°
= 60°
The perimeter will be:
= 4 × 4
= 16 inches.
The length of the diagonal will be:
= 2 × 3.46
= 6.92 = 7
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How can we develop a margin of error through the use of simulation models for random sampling
When using simulation models for random sampling, we can develop the margin of error by multiplying the critical value by the standard error.
What is the margin or error?This is a measure of the error that we get when we use a random sampling model.
It can be found by the formula:
= Critical value x Standard error
If using a z-test, the critical value would be z and the standard error would be (σ / √n). The margin or error would therefore be:
= z (σ / √n)
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If x varies directly as y, and x = 28 when y = 4, find x when y = 8.
Answer:
to find the value of x
x=(8x28)÷4
Answer: x=56
x/y 28/4=x/8
reduce 28/4 to 7/1
7/1 = x/8
cross multiply
x=56
Step-by-step explanation:
Pls answer for brainlest and 50 points PLEASE EXPLAIN
In image
Answer:
r = 163 --> C
Step-by-step explanation:
In a right triangle, the remaining angle is = 180-73-90 = 17
Because n // p so acute angle created by n = 17
r+17 =180 --> r = 180-17 = 163
Question 1- Whats the derivative of: A) f(x)= 4 cos(x) + ln(x+1)
B) f(x)= sec(x) X tg(x)
The derivatives for this problem are given as follows:
a) [tex]f^{\prime}(x) = -4\sin{x} + \frac{1}{x + 1}[/tex]
b) [tex]f^{\prime}(x) = \sec{x}\tan^{2}{x} + \sec^3{x}[/tex].
What is the derivative of the sum?The derivative of the sum is the sum of the derivatives.
In this problem, the function is:
[tex]f(x) = 4\cos{x} + \ln{(x + 1)}[/tex]
Using a derivative table for the derivatives of the cosine and the ln, the derivative of the function is:
[tex]f^{\prime}(x) = (4\cos{x})^{\prime} + (\ln{(x + 1)})^{\prime}[/tex]
[tex]f^{\prime}(x) = -4\sin{x} + \frac{1}{x + 1}[/tex]
What is the product rule?
The derivative of the product is given as follows:
[tex](f(x) \times g(x))^{\prime} = f^{\prime}(x)g(x) + g^{\prime}(x)f(x)[/tex]
In this problem, we have that:
[tex]f(x) = \sec{x}, f^{\prime}(x) = \sec{x}\tan{x}[/tex].[tex]g(x) = \tan{x}, f^{\prime}(x) = \sec^2{x}[/tex].Hence the derivative is:
[tex]f^{\prime}(x) = \sec{x}\tan^{2}{x} + \sec^3{x}[/tex].
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Find the value of 1 + 3 +5+ ... + 125
Answer:
3906
Step-by-step explanation:
(125-1):2+1=63
63x(125+1):2=3906
Which functions have a maximum and are transformed to the left and down of the parent function, f(x) = x2? Check all that apply.
p(x) = 14(x + 7)2 + 1
q(x) = –5(x + 10)2 – 1
s(x) = –(x – 1)2 + 0.5
g(x) = 2x2 + 10x – 35
t(x) = –2x2 – 4x – 3
The functions that have a maximum and are transformed are:
q(x) = –5(x + 10)2 – 1t(x) = –2x2 – 4x – 3What is a function?This is the rule in mathematics that is used to show the relationship that is in existence between variables.
In order to check for the minimum and the maximum, we have to check on the coefficient of the x square. When it is negative, we have a maximum. When it is positive it is a minimum.
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Answer: b and e
Step-by-step explanation: algebra edge 2022 :)
¿What are Equivalent Fractions?
50 points
Answer:
Step-by-step explanation:
Equivalent fractions represent the same value, even though they look different. For example, if you have a cake, cut it into two equal pieces, and eat one of them, you will have eaten half the cake.
Numeric Example= [tex]\frac{2}{2} =\frac{1}{1}[/tex]
[tex]{\huge \underline{{ \fbox \color{red}{A}}{\fbox \color{green}{n}}{\fbox \color{purple}{s}}{\fbox \color{brown}{w}}{\fbox \color{yellow}{e}}{\fbox \color{gray}{r } }}}[/tex]
Equivalent Fractions have the same value, even though they look different.
☆Example :-
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{\tt \dfrac{1}{2} = \dfrac{2}{4} = \dfrac{4}{8} }[/tex]
¿Why are they the same?
Because when you multiply or divide the numerator and denominator by the same amount, the fraction does NOT change.
Remember that :-
Remember that :- The multiplication and division that you apply in the numerator to e must repeat in the denominator.
That's why the fractions are really the same.
◇Watch the process ;
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt \boxed{ \tt \frac{1}{2} = \frac{2}{4} = \frac{4}{8} }[/tex]
That's multiplying
(Image 1)
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \tt\dfrac{18}{36} = \dfrac{6}{12 } = \dfrac{1}{2} }[/tex]
That's Division
(Image 2)
I hope I've helped : )
If r and s represent two numbers, write the following:
53a. Twice the sum of the two numbers
53b. 5% of the difference between the two numbers
Answer:
hope it helps. good day .in case of any question please ask.
Which has a higher cost of credit, a $12,000.00 loan for 3 years at 21.2% interest or a $24,000.00 loan for 3 years at 10.6% interest?
Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. Both the cards have the same cost of credit.
What is simple interest?Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,
SI = PRT
where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.
The interest on $12,000 will be,
SI = $12,000 × 3 × 0.212 = $7,632
The interest on $24,000 will be,
SI = $24,000 × 3 × 0.106 = $7,632
Hence, both the cards have the same cost of credit.
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Estimate 760 X 55 by first rounding each number so that it has only 1 nonzero digit.
Answer:
48000
Step-by-step explanation:
After rounding each number to the criteria stated, we get the question 800 * 60. Multiply the 8 and the 6 and add the same number of zeros that are there right now. this is 48 + "000" so 48000.
Evaluate 3b²-c when b = 1/2 and c = 1/4
Answer:
1/2
Step-by-step explanation:
We are given the expression 3b²-c, and we want to evaluate it if b is 1/2 and c is 1/4.
Because b and c are given values, we can substitute them into the expression as so:
Replace b with 1/2 in the expression.
3(1/2)²-c
Now replace c with 1/4 in the expression.
3(1/2)²-1/4
Now to solve this, we need to use the order of operations, which is usually known as PEMDAS (parentheses, exponents, multiplication, division, addition, subtraction) in the United States, although other countries have different abbreviations.
Regardless, the order of operations tells us that we should start with what is inside parentheses (i.e. if we need to do anything, like multiplying or dividing any numbers that are inside parentheses).
In this case, we don't have anything. So, we should go next to exponents, and we do have an exponent here (1/2 is raised to the second power).
So let's evaluate that.
Raise 1/2 to the second power (multiply it by itself).
1/2 * 1/2 = 1/4
We can substitute (1/2)² with 1/4:
3(1/4) - 1/4
Next, we should take care of any multiplication / division, making sure that we should work left to right
There is one multiplication thing to do: the 3(1/4), which will be 3/4
Replace 3(1/4) with 3/4.
3/4 - 1/4
Now, we can subtract 1/4 from 3/4, as the final two things in PEMDAS are addition and subtraction (A and S). Note that even though while addition is written first, we should always be working left to right, so for example if we had 3 - 4 + 6, we should do 3 - 4 first, THEN add 6 to the result of that. The same is true for multiplication and division.
3/4 - 1/4 = 2/4 = 1/2
The sum of three numbers 157. The third number is 7 less than the firstThe second number is 4 times the third What are the numbers?
Step-by-step explanation:
Let the first number be = x
Let the second number be = 4x -28
Let the third = x-7
x + 4x+ x -28 - 7
6x - 35
6x -35 = 157
6x = 157 +35
6x = 192
x = 32
therefore, x = 32, the second x = 4(32) -28
728 - 28
x = 100
third x = 32 - 7
x = 25.
how can -6 divide by 4 x=12 be solved in one step
Here are the solving steps for the problem.
Given:
[tex]\displaystyle \frac{-6}{4x}=12[/tex]
[1] Multiply both sides of the equation by 4x:
[tex]\displaystyle 4x(\frac{-6}{4x})=(12)4x[/tex]
-6 = 48x
[2] Divide both sides of the equation by 48:
[tex]\displaystyle \frac{-6}{48} = \frac{48x}{48}[/tex]
[tex]\displaystyle x=-\frac{1}{8}[/tex]
I am not sure how to solve the equation in one step, so here is it in two steps. My apologies.
Answer:
[tex] - \frac{1}{8} [/tex]
Step-by-step explanation:
The Algebraic Equation -6 divide by 4x = 12 can be stated mathematically as :
[tex] \frac{ - 6}{4x} = 12 \\ \\ cross \: multiplying \\ \\ 4x \: \times 12 = - 6 \\ \\ 48x = - 6 \\ dividing \: bothsides \: by \: 48 \\ \frac{48x}{48} = \frac{ - 6}{48} \\ \\ x = - \frac{1}{8} [/tex]
what is the common ratio of 3,1,1/3,1/9?
Answer:
mine was D
Step-by-step explanation:
mine was D unless its diffrent
2.5.2 project performance task:trade show booth
The booth space and the product brochures are less than $3000 hence the equation of inequality will be B + P ≤ $ 3000.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Let the booth space be B and the product brochures be P.
Then the equation of inequality will be
B + P ≤ $ 3000
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Complete question:
2.5.2 Project: A Trade Show Booth
The Scenario: Your manager has asked you to help plan your company's participation at a local trade show. You have $3000 to spend on the booth space and product brochures. Use what you know about solving inequalities to prepare the inequality that meets the budget.
Does anyone know the answer to this?
1) m∠1 = 62°, lines t and l intersect (given)
2) ∠1 and ∠4 are vertical angles (intersecting lines form vertical angles)
3) ∠1 and ∠4 are congruent (vertical angles are congruent)
4) m∠1 = m∠4 (congruent angles have equal measure)
5) 62° = m∠4 (substitution)
6) m∠4 = 62° (symmetric property of equality)
11) Gretchen purchased a dress that originally cost $89.99. It was marked down 30% off. What was the cost of the
dress?
O a.) $65.99
Ob.) $63.99
Oc.) $62.99
Od.) $64.99
Least common multiple of 10,20 35
Answer: 140
Step-by-step explanation:
Cheryl invested $1000 on Monday.Each day after that the stock increased 1% of its original value.On Wednesday she was charged an administrative fee of $10. Graph the value of the stock account at the end of each day
The value of the stock account at the end of each day is mathematically given as
x=1010$.
What is the value of the stock account at the end of each day?Generally, The price of the stock would have climbed by 1000 points, which is equal to 0.1 times 1000, or 10 dollars.
Therefore, the price of the stock would be 1010 dollars plus 10 dollars, which is 1020 dollars.
In conclusion, Cheryl was required to pay a ten dollar administrative fee, and this cost would be deducted from the stock price.
Following this logic, the price of the stock would be
x=1020-10
x=1010$.
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What is the value of In e^4?
0 0
O 1
02
04
Answer:
4
Step-by-step explanation:
[tex]In(e^4)[/tex] = [tex]4In(e)[/tex]
= 4 x 1
= 4
The value of the expression ln([tex]e^4[/tex]) is 4.
Option D is the correct answer.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
The natural logarithm (ln) is the inverse function of the exponential function,
[tex]e^x[/tex].
ln([tex]e^4[/tex]) = 4,
since ln([tex]e^4[/tex]) "undoes" the exponentiation of [tex]e^4[/tex].
So the value of ln([tex]e^4[/tex]) is 4.
Thus,
The value of the expression ln([tex]e^4[/tex]) is 4.
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solve for the pattern 7, 11, 2, 18, -7, ?
Answer:
7, 11, 2, 18, -7, 25
2. Find the largest value of s satisfying the condition
The required value of δ = 1/4.
0< |x-1| < δ
| f(x) - 4 | < 1/2 where f(x) = 6 - 2x
Inequality can be define as the relation of equation contains the symbol of ( ≤, ≥, <, >) instead of equal sign in an equation
now
| f(x) - 4 | < 1/2
|6 - 2x - 4 | <1/2
| 2-2x | < 1/2
| 1 - x | < 1/4
| x - 1 | < 1/4
since modulus function always give positive values.
0 < | x - 1 | < 1 /4
The required value of δ = 1/4.
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Question
You want to find the area of the front of a house, whose shape is a triangle on top of a rectangle with
a width of 8. The triangle's height is 7 and the rectangle's height is 10. What is the total area of the
front of the house? Do not include units in your answer.
Answer:
108
Step-by-step explanation:
if the width of the rectangle is 8, and the triangle is on the width of the rectangle, then the base of the rectangle is 8. the height is 7, so we use the formula area = height * base / 2 to find that the area of the triangular portion is 28. then, we find the area of the rectangle by doing 10 * 8(height * width) for a value of 80. the total area of the front of the house is 28 + 80: 108.
The graph shown below expresses a radical function that can be written in the form f(x)= a(x + k)^1/n +C. What does the graph tell you about the value of c in this function?
Answer:
C. c is less than zero
Step-by-step explanation:
The parent radical function y=x^(1/n) has its point of inflection at the origin. The graph shows that point of inflection has been translated left and down.
Function transformationThe transformation of the parent function y=x^(1/n) into the function ...
f(x) = a(x +k)^(1/n) +c
represents the following transformations:
vertical scaling by a factor of 'a'left shift by k unitsup shift by c unitsApplicationThe location of the inflection point at (-3, -4) indicates it has been shifted left 3 units, and down 4 units. In the transformed function equation, this means ...
k = 3c = -4The graph says the value of c is less than zero.
__
Additional comment
Apparently, the value of 'a' is 2, and the value of n is 3. The equation of the graph seems to be ...
f(x) = 2(x +3)^(1/3) -4
Please help answering this question
Answer:
DF = 3
Step-by-step explanation:
BC = DF
Which mean D is (0,2) and F is (3,2)
Here, this is clear that y-intercept is 2
DF = D(x) + F(x) = 0 +3 = 3
b. Miguel tiene 104 canicas grandes, 117
medianas y 130 pequeñas. Si quiere
repartirlas en grupos iguales con la
mayor cantidad de cada tipo de cani-
cas, ¿cuántos grupos podrá formar?
¿Cuántas canicas de cada tipo habrá
en cada grupo?
Considerando la definición de divisor común mayor:
si Miguel quiere repartir las canicas en grupos iguales con la mayor cantidad de cada tipo tendrá 13 grupos.en cada grupo habrá 8 canicas grandes, 9 canicas medianas y 10 canicas pequeñas.Definición de divisorLos divisores de un número natural son los números naturales que lo pueden dividir, resultando de cociente otro número natural y de resto 0. Ser divisor es lo recíproco a ser múltiplo.
En otras palabras, un número es divisor de otro si está contenido una cantidad entera de veces. Por lo tanto, al dividir el número por el divisor el cociente debe resultar un número entero (que no sea un número decimal) y el residuo o resto de la división sea 0.
Divisor común mayorSe denomina máximo común divisor al mayor número que divide exactamente a dos o más números a la vez.
En otras palabras, el divisor común mayor es el mayor de los divisores que tienen en común dos o más números.
Para calcular el divisor común mayor se debe realizar los siguientes pasos:
Descomponer cada número en factores primos.Después, señalar los factores comunes (números primos que aparecen en todos los números).A continuación, en cada uno de los comunes, escoger el factor con menor exponente (factor que aparece la menor cantidad de veces).Por ultimo, multiplicar los factores elegidos.Cantidad de gruposPara calcular la cantidad de grupos se debe calcular el divisor común mayor. Para ello, en primer lugar se descomponen los números:
104= 2×2×2×13= 2³×13117= 3×3×13= 3²×13130= 2×5×13El factor común a todos los números es el número 13. Esto indica que si Miguel quiere repartir las canicas en grupos iguales con la mayor cantidad de cada tipo tendrá 13 grupos.
Cantidad de canicas de cada tipo en cada grupoPara esto se deberá dividir la cantidad de cada tipo de canica por la cantidad de grupos formados, que en este caso es 13. Esto es:
104 canicas grandes÷ 13 grupos= 8 canicas grandes117 canicas medianas÷ 13 grupos= 9 canicas medianas130 canicas pequeñas÷ 13 grupos= 10 canicas pequeñas
Finalmente, en cada grupo habrá 8 canicas grandes, 9 canicas medianas y 10 canicas pequeñas.
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