Answer:
There is not sufficient evidence to support the conclusion that senators are average younger than 60.35
Step-by-step explanation:
Given a simple random sample, the size is 40 senators.
Since the relevant statistic is the sample mean, 60.35 years.
Calculate t as:
[tex]t=\frac{\bar{x}-\mu_{\bar{x}}}{\frac{s}{\sqrt[]{n}}}[/tex]*Significance level is 0.05.
[tex]\begin{gathered} t=\frac{60.35-55.4}{\frac{6.5}{\sqrt[]{40}}} \\ t=4.82 \end{gathered}[/tex]Area of 0.05, one-tail yields t=1.685.
Since t=4.82 does not fall in the critical region bounded, we fail to reject the null hypothesis.
There is not sufficient evidence to support the conclusion that senators are average younger than 60.35
What table represents a function?
Answer:
Step-by-step explanation:
The bottom right box.
please help i don’t get this one
Answer: 1.001 x 10^3
Step-by-step explanation:
The probability of passing the math class of Professor Chesley is 58%, the probability of passing Professor Lacava's physics class is 24%, and the probability of passing both is 19%What is the probability of passing one or the other?
The probability of passing one test or the other is given by:
0.63 = 63%.
What is a Venn probability?In a Venn probability, two non-independent events are related with each other, as are their probabilities.
The "or probability" between these two events is given by the rule presented as follows:
P(A or B) = P(A) + P(B) - P(A and B)
In the context of this problem, these events are given as follows:
Event A: Passing the math class of Professor Chesley.Event B: Passing the physics class of Professor Lacava.The probabilities of each event and the and probability are listed as follows:
P(A) = 0.58, P(B) = 0.24, P(A and B) = 0.19.
Hence the probability of passing one test or the other is calculated as follows:
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 0.58 + 0.24 - 0.19 = 0.63 = 63%.
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value of x in the diagram shown is:
Use the slope formula to find the slope between the given two points.
(5, 3) and (5, -9)
Answer:
Undefinded
Step-by-step explanation:
The slope between two points is the RISE/RUN.
Take 5he two given points to calculate the RISE and RUN:
(5,3) and (5,-9)
RISE: (-9 - 3) = -12
RUN (5 - 5) = 0
RISE/EUN = 12/0 = UNDEFINED
The value of y varies directly with x. When x = 5, y = 12. What is the value of x when y = 1?
When the value of y varies directly with x and x = 5, y = 12 then, the value of x when y = 1 is 5/12.
What is direct variation?
The relationship between two variables in which one is a constant multiple of the other is referred to as direct variation. For instance, two variables are said to be in proportion when one affects the other. b = ka is the equation if b is directly proportional to a. (where k is a constant). When two variables are coupled in a way that ensures the ratio of their values never changes, this relationship is referred to as being in direct variation. Different mathematical structures are used to express direct variation. Since the ratio of y to x never changes, y and x fluctuate directly in equation form.
As given in the question,
when x = 5, y = 12,
x and y varies directly, it means they are directly proportional:
y ∝ x
y = kx {here, k is a constant}
Putting the value of x and y, and finding the value of k:
k = 12/5
Now, we need to find x when y = 1. so,
y = kx
putting the values,
1 = (12/5)x
x = 5/12
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1. The distance between two cities on the map was 6.5 cm. If the scale of the picture is 1:5000000, find the distance between the two cities.
2. How many centimeters can be used to represent a distance of 650 km on a map with a scale of 1:1500000?
3. If the distance between Ulaanbaatar and Choibalsan is 630 km, and the distance between these cities is shown on the map as 7 cm, find the scale of the map.
Based on the information provided about this map, we have the following answers:
The distance between the two cities is equal to 325 km.The number of centimeters can be used to represent a distance of 650 km on a map with a scale of 1:1500000 is 43.333 cm.The scale of the map is equal to 1:9,000,000.What is scale factor?A scale factor can be defined as the ratio of two (2) corresponding length of sides or diameter in two similar geometric figures such as equilateral triangles, river, planets in our solar system, etc.
Mathematically, the scale factor of a figure such as a map can be calculated by using this formula:
Scale factor = Dimension of image/Dimension of original figure
In Mathematics, an appropriate conversion factor to an equal value must be used when it is necessary to perform any mathematical conversion of units.
Conversion:
1 = 5000000
6.5 = X
Cross-multiplying, we have:
X = 6.5 × 5000000
X = 32,500,000 cm
X = 325 km.
Question 2.The amount of centimeters that can be used to represent a distance of 650 km on a map with a scale of 1:1500000 is given by:
Conversion:
1 = 1500000
X = 6.5
Therefore, we have:
X = 650/15
X = 43.333 cm.
Question 3.We would determine the scale of the map as follows;
Conversion:
7 cm ⇒ 63,000,000 cm = 630 km
Therefore, the scale of the map is given by:
Scale = 7:63,000,000 = 7/63,000,000
Scale = 1/9,000,000
Scale = 1:9,000,000
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Solve using Substitution
9x+10y=1
y=-8
(?,?)
Answer:
x=9,y=8
Step-by-step explanation:
Step 1: Substitute y=-8 into equation 1
9x+10(-8)=1
9x+(-80)=1
9x=1+80
9x=81
Step 2: Divide both sides by the coefficient of x which is 9 then,
x=9
Step 3: Also substitute x=9 into equation 1
9(9)+10y=1
81+10y=1
10y=1-81
10y=-80
Step 4:Divide both sides by 10 then,
y=-8
hi help please thanks
In linear equation, x = 9 is the value of Maggie that she made.
What is linear equation in math?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.4x + 2 = 7x - 25
7x - 4x = 2 + 25
3x = 27
x = 27/3
x = 9
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Dada una sucesión aritmética, el 75° término, a75 es igual a 556, y el 8° término, a8 es igual a 87. Hallar el valor del 36° término, a36
The value of the 36th term of the arithmetic sequence is 283.
How to calculate the value?It should be noted that an arithmetic sequence illustrate the common difference between the terms.
The following can be deduced from the information:
75th term = a + 74d = 556
8th term = a + 7d = 87
Subtract the equations
(74d - 7d) = 556 - 87
67d = 469
Divide
d = 469/67
d = 7
The first term(a) will be:
a + 7d = 87
Recall d = 7
a + 7(7) = 87
a + 49 = 87
a = 87 - 49
a = 38
Therefore, the 36th term will be:
a + 35d.
a = first term
d = common difference
38 + 35(7)
= 38 + 245
= 283
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Math homework help 2.0
Answer:
Step-by-step explanation:
f(x)=-1/4x-2
Pls help:
What is the value of x?
Enter your answer in the box.
x =
The value of x in the given diagram is 50°
Calculating angles and values of variablesFrom the question, we are to determine the value of x
From the Vertically opposite angles theorem, we have that vertically opposite angles are congruent.
Thus,
From the given diagram, we can write that
[2(x + 10)]° = (3x - 30)°
Now, we will solve for x
[2(x + 10)]° = (3x - 30)°
2(x + 10)° = (3x - 30)°
2x + 20° = 3x - 30°
20° + 30° = 3x - 2x
50° = x
Hence,
x = 50°
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Owen is working two summer jobs, making $25 per hour tutoring and making $10
per hour clearing tables. In a given week, he can work no more than 12 total hours
and must earn a minimum of $150. Also, he must work a maximum of 9 hours
tutoring and a maximum of 4 hours clearing tables. If a represents the number of
hours tutoring and y represents the number of hours clearing tables, write and solve
a system of inequalities graphically and determine one possible solution.
The system of inequalities are
x + y = 12,
25x + 10y ≤ 150
x ≥ 9,
y ≥ 4 and the graph of the inequality is attached below.
Inequality:
Inequality refers the relationship between two values that are not equal is defined by inequalities. Inequality means not equal.
Given,
No. of summer job Owen working = 2 (tutoring and clearing tables)
Cost per hour (tutoring) = $25
Cost per hour (clearing tables) = $10
In a week,
Total working hour = 12
Minimum Amount earned = $150
Maximum hours (tutoring) = 9
Maximum hours (clearing tables) = 4
Here we need to find the system of inequalities and we have to plot the graph for it.
Then we need to find one possible solution for it.
Let us consider x be the number of hours for tutoring and y be the number of clearing table.
So, the total number of working hours,
x + y = 12
And the amount earned in the week,
25x + 10y ≤ 150
And we also know that,
x ≥ 9 and y ≥ 4.
The graph of the equation is attached below.
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8. What are the values of x and y?
X
36
Every year 3% of university students drop out of their course at
a University. This year 12 people dropped out. How
many people started at the beginning of the year?
Answer:400
Step-by-step explanation: 12/3= 4 4x100= 400
Write the following series in sigma notation. 6 + 8 + 10 + 12 + 14 + 16 + 18
The sigma notation of the series is [tex]\sum_{n=3}^9(2n)[/tex]
How to write the sigma notation?
This is a series of even numbers which is represented as 2nTo get the first number of the series ,2n = 6
n = 3
To get the last number of the series,2n = 18
n = 9
The limits are [3,9]
Thus the sigma notation can be represented as,[tex]\sum_{n=3}^9(2n)[/tex] = 84
What is a sigma notation?
Summation, often known as sigma notation, is a concise way to represent a series. The sum is denoted by the capital letter ∑ in Greek. The summation index must be replaced with consecutive integers starting with the first value and ending with the last value in order to produce the terms of a series provided in sigma notation.To learn more about sigma notation, refer:
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I don't get this question. Please help.
Answer: M x X
P x E
YW x RK
Step-by-step explanation:
pls help i need -3x+20+-10
Answer:
-3x + 10
Step-by-step explanation:
you add like terms of 20 and negative 10 to simplify to -3x +10
What’s 2/6 + 3/4 pls help me
The initial expression is:
[tex]\frac{2}{6}+\frac{3}{4}[/tex]We need to use the addition of fractions rule, and we obtain:
[tex]\begin{gathered} \frac{2}{6}+\frac{3}{4}=\frac{2\cdot4+6\cdot3}{6\cdot4}=\frac{8+18}{24}=\frac{26}{24}=\frac{2\cdot13}{2\cdot12}=\frac{2}{2}\cdot\frac{13}{12}=1\cdot\frac{13}{12} \\ \Rightarrow\frac{2}{6}+\frac{3}{4}=\frac{13}{12} \end{gathered}[/tex]The answer is 13/12
Why would knowing the Pythagorean identity sin2x + cos2x = 1 and the sum identities allow you to prove all the other identities you have seen in this lesson?
The sum identities in trigonometry are cos^2(x)+sin^2(x)=1
sec^2-tan^2(x)=1
cosec^2(x)-cot^2(x)=1
What is Trigonometry?Trigonometry: Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles. Trigonometry is found all throughout geometry, as every straight-sided shape may be broken into as a collection of triangles
Let's prove using the angle addition formula for cosine:
cos(α+β)=cos(α)cos(β)-sin(α)sin(β)
we know that sin(-x)= -sin x and
cos(-x)=cos x
we need to proceed to the proof ,
let α=x and β=-x
cos(x+(-x))=cos(x)cos(-x)-sin(x)sin(-x)
cos(0) = cos(x)cos(x)+sin(x)sin(x)
cos^2(x)+sin^2(x)=1
Hence, it is proved
to prove another identity i.e., sec^2-tan^2(x)=1
start from cos^2(x)+sin^2(x)=1
divide both the sides by cos^2(x)
cos^2(x)/cos^2(x)+sin^2(x)/cos^2(x)=1/cos^2(x)
1+tan^2(x)=sec^2(x)
sec^2-tan^2(x)=1
Hence, it is proved
to prove another identity i.e., cosec^2(x)-cot^2(x)=1
start from cos^2(x)+sin^2(x)=1
divide both sides by sin^2(x)
cos^2(x)/sin^2(x)+sin^2(x)/sin^2(x)=1/sin^2(x)
cot^2(x)+1=cosec^2(x)
cosec^2(x)-cot^2(x)=1
Hence, it is proved
The sum identities in trigonometry are proved
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2) Roni donates 10% of her paycheck to a local charity and puts 15% of her
paycheck in a savings account. If Roni's paycheck is $2,020.00, which of the
following is the amount which will go to charity and savings?
A. $505
B. $909
C. $202
D. $303
Step-by-step explanation:
amt. means amount
explaination in my workings
hope this helps!!
explain how to expand (x + 3)7 using the binomial theorem.
According to the binomial theorem, the binomial (x + 3)⁷ is equal to the septimic polynomial x⁷ + 21 · x⁶ + 189 · x⁵ + 945 · x⁴ + 2835 · x³ + 5103 · x² + 5103 · x + 2187.
How to expand the power of a binomial by using binomials theorem
Binomial theorem offers a brief form to expand the power of a binomial, that is, an algebraic expression of the form (a + b)ⁿ, where n is a natural number. The complete formula is shown below:
(a + b)ⁿ = Σ {n! / [k! · (n - k)!]} · [tex]a^{n-k}[/tex] · [tex]b^{k}[/tex], for k ∈ {0, 1, 2, ..., n - 1, n}
If we know that a = x, b = 3 and 7, then the expanded form of the power of the binomial is:
(x + 3)⁷ = [7! / (0! · 7!)] · x⁷ · 3⁰ + [7! / (1! · 6!)] · x⁶ · 3 + [7! / (2! · 5!)] · x⁵ · 3² + [7! / (3! · 4!)] · x⁴ · 3³ + [7! / (4! · 3!)] · x³ · 3⁴ + [7! / (5! · 2!)] · x² · 3⁵ + [7! / (6! · 1!)] · x · 3⁶ + [7! / (7! · 0!)] · x⁰ · 3⁷
(x + 3)⁷ = x⁷ + 7 · x⁶ · 3 + 21 · x⁵ · 3² + 35 · x⁴ · 3³ + 35 · x³ · 3⁴ + 21 · x² · 3⁵ + 7 · x · 3⁶ + 3⁷
(x + 3)⁷ = x⁷ + 21 · x⁶ + 189 · x⁵ + 945 · x⁴ + 2835 · x³ + 5103 · x² + 5103 · x + 2187
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Answer:
To write the coefficients of the 8 terms, either start with a combination of 7 things taken 0 at a time and continue to 7 things taken 7 at a time or use the 7th row of Pascal’s triangle.For the first term, write x to the 7th power and 3 to the 0 power. Then decrease the power on x and increase the power on y until you reach x to the 0 and y to the 7.Simplify by evaluating the coefficients and powers of 3.
Write an equation of a line that is perpendicular to y = 4x + 8 and passes through (−8, 4).
y equals negative one-fourth times x minus 7
y equals negative one-fourth times x plus 2
y = 4x + 24
y = 4x + 36
The equation of a line that is perpendicular to y = 4x + 8 and passes through (−8, 4) is y = - 1 / 4 x + 2 (y equals negative one-fourth times x plus 2)
How to find equation of a line?The equation of the line is perpendicular to y = 4x + 8 and passes through (-8, 4).
Therefore, the equation of a line can be represented as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore, perpendicular lines follows the rule below:
m₁ m₂ = -1
4m₂ = -1
m₂ = - 1 / 4
Hence, let's find the y -intercept using (-8, 4)
y = - 1 / 4 x + b
4 = - 1 / 4 (-8) + b
4 = 2 + b
b = 4 - 2
b = 2
Therefore, the equation is y = - 1 / 4 x + 2
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Answer: D.) y = 4x + 4
Step-by-step explanation:
just did the assignment
Which expression is equivalent to -12(3x -3/4)?
Answer:
- 36x + 9
Step-by-step explanation:
- 12(3x - [tex]\frac{3}{4}[/tex] ) ← multiply each term in the parenthesis by - 12
= - 36x + 9
Answer:
-36x + 9
Step-by-step explanation:
Given expression:
[tex]-12\left(3x-\dfrac{3}{4}\right)[/tex]
Apply the distributive rule:
[tex]\implies -12 \cdot 3x -12 \cdot -\dfrac{3}{4}[/tex]
Multiply -12 and 3x:
[tex]\implies -36x -12 \cdot -\dfrac{3}{4}[/tex]
Apply the rule -a(-b) = ab:
[tex]\implies -36x +12 \cdot \dfrac{3}{4}[/tex]
Convert 12 into a fraction:
[tex]\implies -36x +\dfrac{12}{1} \cdot \dfrac{3}{4}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{b} \cdot \dfrac{c}{d}=\dfrac{ac}{db}}:[/tex]
[tex]\implies -36x +\dfrac{36}{4}[/tex]
Divide the numbers:
[tex]\implies -36x +9[/tex]
Therefore, the equivalent expression to the given expression is:
-36x + 9Q7: A farmer wants to build a metal fence to enclose his livestock. The fence's vertices are represented by
points A(4,-4), B(-4,-4), C(-4, 3), D(1, 3), E(1,-1), and F(4,-1). Each unit in the coordinate plane
represents 1 meter in reality. Since a gate is to be added between points A and F. the farmer will not use
metal fencing on that side. What is the total number of meters of metal fencing the farmer needs?
Answer:down below
Step-by-step explanation:A square gives the greatest area. If the river were not there, you would divide 1700 by 4 to get a square 425 feet by 425 feet. Because of the river, add 425 feet to the side opposite the river to get a rectangle 425 feet by 850 feet.
Now for the algebra that you need.
P=2l+2w but there is only one length.
P=l+2w
1700=l+2w
1700-2w=l
A=lw
A=(1700-2w)w
A=1700w-2w2
This is a parabola that opens downward so there is a maximum point, the vertex, which is (h,k).
h=-b/2a is the "maximizing point" and k is the maximum area
-b/2a=-1700/(-4)
-b/2a=425 feet
One width will be 425 feet, the length will be (425+425)=850 feet, and the second width will also be 425 feet.
A=lw
The maximum area will be A=850*425=361,250 square feet.
Notice that if you substitute 425 into the equation A=1700w-2w2 you will get the same answer.
1700*425-2*4252
722,500-2*180,625
722,500-361,250
Given the equation 4x + 12 = 64: part a: write a short word problem about a purchase made to illustrate the equation. (6 points) part b: solve the equation showing all work. (4 points) part c: explain what the value of the variable represents. (2 points)
From the equation 4x + 12 = 64, we have that:
a. The problem is: An amount was quadrupled then added by 12, resulting in a final amount of 64.
b. The solution to the equation is x = 13.
c. The solution of x = 13 represents the initial amount.
Context of the equation 4x + 12 = 64The amount x is unknown, hence the problem begins with the unknown amount x.
4x means that the amount was quadrupled.4x + 12 means that 12 was added to the amount.4x + 12 = 64 means that the final amount has a value of 64.Which means that the problem can be summarized as:
An amount was quadrupled then added by 12, resulting in a final amount of 64.
The equation can be solved isolating x as follows:
4x + 12 = 64
4x = 64 - 12
4x = 52
x = 52/4
x = 13.
Meaning that the initial amount was of 13.
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I did not really understand can some one help
Answer:
62 pages in each notebook
Step-by-step explanation:
she filled 372 pages in 6 notebooks , then
372 ÷ 6 = 62
there are 62 pages in each notebook
12. The tallest platform for Olympic diving is
33 feet above the water. After a diver
completes a dive, they reach 14 feet below
the water. What is the distance between the
height of the platform and the depth of the
diver? (Example 3)
The distance between the height of the platform and the depth below water is 47ft . The concept of depth describes how far something extends.
How to calculate depth ?A deep area in a body of water is what the word "DEPTH" means.
Ocean depth is most frequently and quickly measured using sound. Sonar, which stands for sound navigation and range, is a technique that allows ships to map the topography of the ocean below. The instrument uses sound waves to send to the ocean's bottom and time how long it takes for an echo to come back.
Water depth is the distance in feet between the ocean's surface and bottom, as determined by mean lower low water.
Use the following formula for measuring ocean depth.
D = V Times 1/2 T D
Depth (in meters) T= Time (in seconds) V = 1507 m/s (speed of sound in water)
In the question we have,
Platform to surface of water = 33ft
Platform to depth below water = 33+14 = 47ft
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A local amusement park is advertising their Season pass prices for the 2023 season. A single Pass is $50 per day plus $10.00 per day for parking. A silver pass is $120 for summer season plus $20.00 per day for preferred parking. When would it be worth it to buy a Silver pass instead of paying for single days?
(please help asap) ** you can solve with substitution or elimination**
The linear inequality leads us to the conclusion that the silver pass will be more advantageous if a visitor stays at the theme park for more than three days.
Let the number of days be x.
So, cost of single pass for one day is 50 +10 = $60
cost of single pass for x days is 60x.
cost of silver pass for one day is 120 +20 = $140
cost of silver pass for x days is 120+20x.
Now, for silver pass to be worth to buy instead of single pass will be when it costs lesser than that of the single pass.
So,
Cost of silver pass < cost of single pass
120 + 20x < 60x
120 < 40x
x>3,
So, we can say conclude from the linear inequality that the silver pass will be more beneficial if someone is staying at amusement park for more than 3 days.
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Find the volume of the composed figure. 6 cm 16 cm Som Enter the correct number in the box. Hint cu cm
Let's cut the given solid into two parts to easily get its total volume:
Let's determine the volume of figure A:
[tex]\text{ Volume = L x W x H}[/tex][tex]\text{ = 6 x 8 x (16-8) = 6 x 8 x 8}[/tex][tex]\text{ Volume of Figure A = 384 cm}^3[/tex]Let's determine the volume of figure B:
[tex]\text{ Volume = L x W x H}[/tex][tex]\text{ = 24 x 8 x 6}[/tex][tex]\text{ Volume of Figure B = 1,152 cm}^3[/tex]Let's add the volume of the A and B to get the total volume of the given figure.
We get,
[tex]\text{ Total Volume = Volume Figure A + Volume of Figure B}[/tex][tex]\text{ = 384 + 1,152}[/tex][tex]\text{ Total Volume = 1,536 cm}^3[/tex]Therefore, the volume of the figure is 1,536 cm³.
