One of the six countries sent 41 representatives to the congress.
What, in the simplest words, is the Congress?
The Congress is our country's legislative body, which drafts our laws. The United States Senate and the United States House of Representatives are the two branches of Congress.
Each state has two U.S. Senators and a minimum of one U.S. Representative; the number of U.S. Representatives that can be elected depends on the number of citizens in the state.
(1) One of the six countries sent 41 representatives to the congress
(2) Country A sent fewer than 12 representatives to the congress
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Given the vector u equal to 7 (cos 310°, sin 310°) and vector v equal to
2 (cos 115°, sin 115°), find the sum u + v and write your answer in magnitude
and direction form with the magnitude rounded to the nearest tenth and the
direction rounded to the nearest degree, 0° ≤ 0 < 360°.
To find the sum of vectors u and v, we can add their components separately:
(u + v)x = (7cos 310° + 2cos 115°)
(u + v)y = (7sin 310° + 2sin 115°)
Using a calculator to evaluate these expressions, we get:
(u + v)x = -2.16
(u + v)y = 8.48
The magnitude of the sum vector u + v can be found using the Pythagorean theorem:
|u + v| = √((u + v)x^2 + (u + v)y^2)
= √(-2.16^2 + 8.48^2)
= √(72.3584)
= 8.51
The direction of the sum vector u + v can be found using the inverse tangent function:
θ = tan^(-1)((u + v)y / (u + v)x)
= tan^(-1)(8.48 / -2.16)
= tan^(-1)(-3.928571428571429)
= 143.13°
Rounding the magnitude to the nearest tenth and the direction to the nearest degree, we get:
u + v = 8.5 (cos 143°, sin 143°)
Therefore, the sum of vectors u and v is equal to 8.5 (cos 143°, sin 143°).
If you rent a car from Caleb's Cars, you'll pay a $61 fee
and $24 per day. At Vinny's Vehicles, you'll pay a $105 fee and $20 per day. Determine the number of days you can rent a car from either place and pay the same amount. Use substitution or elimination. Thank you:)
The number of days to rent a car at either place and pay thesame amount is 11 days
What is Simultaneous equation?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time.
Let the number of days to repay after a down payment be x and the y represent the total payment.
Therefore 61+24x= y equation 1
105+ 20x = y equation 2
subtract equation 1 from 2
105-61+20x-24x= 0
44-4x= 0
4x = 44
divide both sides by 4
x= 44/4
x= 11 days
therefore the number of days to rent a car at either places and pay thesame amount is 11 days
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What are the equation in slope of the line that is perpendicular to the Y axis and goes through the point (-2,3)?
A. X=-2, slope is undefined
B. X=3, slope is undefined
C. Y=3, slope is 0
D. X=-2, slope is 0
Please help. Thank you
Answer:
C
Step-by-step explanation:
A line perpendicular to the y-axis is a horizontal line
Horizontal lines have slope = 0
answer C y = 3 slope = 0
write an equation of the line, passing through the points (-5,-25) , (0,0), and (3,15)
Answer:
y =5x
Step-by-step explanation:
y = 5x
Because the slope is 5 and the y-intercept is 0.
8. Critique Reasoning Franco made this graph to
show the equation y=-x. Is the graph correct?
Explain.
Answer:
No
Step-by-step explanation:
The graph should be a line with negative slope, but the given graph is of a line with positive slope
Here are the ingredients needed to make 8 pancakes.
James makes 24 pancakes.
Pancakes
Ingredients to make 8 pancakes
250 ml milk
1 egg
140 g flour
5 g butter
a) Work out how much milk he needs.
Using proportions, James need 750ml for 24 pancakes
ProportionProportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
To find the amount of milk James need, we need to use proportions.
8 pancakes = 250ml milk
24 pancakes = x
cross multiply both side and make x the subject of formula
8 × x = 24 × 250
8x = 6000
Divide both sides by coefficient of x
8x / 8 = 6000 / 8
x = 750
He needs 750 ml of milk
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Divide (25)1,658.To find the quotient, start by dividinginto____.
On dividing 1658 by 25 , the quotient is equal to 66.32.
As given in the question,
Dividend is equal to 1,658
Divisor is equal to 25
Unit place value of 1658 is equal to 8.
25 is not a factor of 1658
Smallest number to 1658 divisible by 25 is 1650
Divide 1658 by 25 we get remainder
Dividend = ( Divisor × quotient) + remainder
1658 = 1650 + 8
= ( 25 × 66 ) + 8
Remainder is equal to 8
Quotient is equal to 66
In decimal form
1658 ÷ 25
= 66.32 is quotient.
Therefore, the quotient of dividing 1658 by 25 is equal to 66.32.
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Answer:
check this one
Step-by-step explanation:
this is the answer
6. Which is equivalent to the following expression?
(3p² +5pq-q²) + (p² +3pq-2q
2
9²)
O3p² +8pq-3q²
O4p² +8pq+q²
O4p4 +8pq-3q
O4p²+8pq-3q²
(1 point)
Answer:
Step-by-step explanation:
5
Find the x-intercept of the line 5x + 17y = -25
x - intercept =
Find the y-intercept of the line 6x - 7y = -21
y - intercept =
Answer: To find the x-intercept of a line, we set y equal to 0 and solve for x. To find the y-intercept of a line, we set x equal to 0 and solve for y.
For the line 5x + 17y = -25, we set y equal to 0 to find the x-intercept:
0 + 17y = -25
17y = -25
y = -25/17
Since we set y equal to 0, the x-intercept is (0, 0).
For the line 6x - 7y = -21, we set x equal to 0 to find the y-intercept:
6x - 7y = -21
-7y = -21
y = 21/7
Since we set x equal to 0, the y-intercept is (0, 21/7).
Therefore, the x-intercept of the line 5x + 17y = -25 is (0, 0) and the y-intercept of the line 6x - 7y = -21 is (0, 21/7).
The low temperature on Saturday was 10 degrees below zero degrees Celsius. On Sunday, the low temperature was 30 degrees
warmer.
Which two statements apply to the low temperature on Sunday?
A Temperature on Sunday was 40°C.
B
C
Temperature on Sunday was 20°C.
The temperature on Sunday was 20 degrees below zero degrees Celsius.
The temperature on Sunday was zero degrees Celsius.
L
E
The temperature on Sunday was 20° C
You receive paychecks every two weeks. Your first paycheck is for $217. The second is for $258. The third is for $229. What is the combined value of these three paychecks?
Answer:
The combined value is $704
If you want the average pay as well it is about $235
Step-by-step explanation:
The problem asks for the combined value of the three paychecks. So all you have to do is add them to get 704.
I found the average value by adding them to 704 then dividing it by 3. The 3 came from the amount of values we have which is 3 paychecks. So we divide the total cost by 3 to get 235.
in a paired test, a factor is what you are testing to see the effect of because its effect is unknown. group of answer choices true false
True, In a paired test, a factor is what you are testing to see the effect of because its effect is unknown.
The paired t-test is a technique for determining whether or not the mean difference between two measurement pairs is zero. When your data values are paired measurements, you can apply the test.
The dependent samples t-test, paired difference t-test, matched pairs t-test, and repeated-samples t-test are other names for the paired t-test. You might not be able to test for normality if your sample sizes are too small. You might have to rely on your comprehension of the information. You might also do a nonparametric test that doesn't make the assumption of normality.
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Name 3 biotic factors in a marine ecosystem
Answer:
Biotic factors of a marine ecosystem typically include algae, plankton, bacteria, seaweed, corals, fish, sharks, seals, whales, penguins and jellyfish.
Step-by-step explanation:
i hope this answer helped
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A quantity decreases by 2% for each of 10 years. What is its percentage decrease over the 10-year period? (Round your answer to two decimal places.
Answer:
20%
Step-by-step explanation:
2 x 10 = 20
20%
do you think it makes sense to use the statistician's model to predict the calories in food items from the fast food restaurant quiteaburger? explain why or why not.
The statistician model makes sense to predict the calories in food items.
What is statistician's model ?A mathematical model called a statistical model contains a collection of statistical presumptions about how sample data are produced (and similar data from a larger population). A statistical model simulates the process of creating data, frequently in a highly idealised form.
Yes it makes sense to use the statistician model to predict calories calories in food items because the test of the overall model I.e F test is significant at any level of significance because the p value (2.2 e^-16) is approximately zero which indicates that the model Is significant.
And also the individual test of each variable are all significant at any significance level (alpha) with p values ( 2e^-16, 2e^-16, 1.36e^-6).
Thirdly we can say of the strength of the relationship between calories and the independent variable through the R value = √R square = √0.929 = 0.9638 which indicates a strong relationship between them.
Therefore, the statistician model makes sense to predict the calories in food items.
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NEED HELP!! Can someone help me solve this puzzle I think I have that first two right?
Reflection of point 1 over X axis is (-4, -2)
Reflection of point 2 over Y axis is (2, 3)
Reflection of point 3 over x = 1 is (2, 1)
Reflection of point 4 over y = x is (2, -1)
What is Reflection of a point?
A reflection point occurs when a figure is constructed around a single point known as the point of reflection or center of the figure. For every point in the figure, another point is found directly opposite to it on the other side.
According to the given question:
1. Reflection of point 1 over X axis (x, -y) ⇔ (x, y)
∴ Reflection of (-4, 2) over X axis is (-4, -2)
2. Reflection of point 2 over Y axis (x, y) ⇔ (-x, y)
∴ Reflection of (-2, 3) over Y axis is (2, 3)
3. Reflection of point 3 over x = 1
∴ Reflection of (-2, 1) over x = 1 axis is (2, 1)
4. Reflection of point 4 over y = x is (x, y) ⇔ (y, x)
∴ Reflection of (-1, 2) over X axis is (2, -1)
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What is √73 in exponential form?
O
314
7
DONE
Answer:
To write √73 in exponential form, we can use the fact that the square root of a number is the same as that number to the power of 1/2. Thus, we can write √73 as 73^(1/2).
Here's how we can show this using algebraic steps:
First, we can write the square root as a fractional exponent:
√73 = 73^(1/2)
Next, we can rewrite the fractional exponent using the rule that says that a^(m/n) = (a^m)^(1/n):
√73 = (73^1)^(1/2)
Finally, we can simplify the expression by evaluating the power of 1:
√73 = (73)^(1/2) = 73^(1/2)
Therefore, √73 can be written in exponential form as 73^(1/2).
Which graph represents the solution to 5 + 8x < 3 (2x+4)?
Graph (D) represented the inequality solution of 5+x<3(2x+4).
What do we mean by the graph?The set of ordered pairs is the graph of a function f in mathematics, where These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.
To develop a graph is to make a diagram that depicts the relationship between two or more objects.
Make a sequence of bars on graph paper as an example of a graph.
So, we have the inequality:
5 + 8x < 3 (2x+4)
Now, we need to plot this on the graph:
(Refer to the graph attached below)
We can easily tell that this is identical to graph sin option (D).
Therefore, graph (D) represented the inequality solution of 5+x<3(2x+4).
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how to determine the intercepts of the line with -5x+9y=-18
Answer:
-5x+9y=-18
Dividing both sides by -18
-5x/-18+9y/-18=-18/-18
5x/18-y/2=1
x/(18/5)-y/2=1. eqn(i)
eqn (i) is comparing with x/a+y/b=1, we get
x - intercept (a) =18/5
y-intercept (b) = -2
Alex, an eighth grader, and Eric, a seventh grader, need to determine who came closer to their grade’s state record for the triple jump. Alex jumped 39.75 feet and
Eric jumped 37 feet and 1 1 inches. Who was closer to the state record if the 4
eighth-grade record is 42.25 feet and the seventh-grade record is 39 feet 3 inches?
The distance Alex jumped and the distance Eric jumped compared with the state records indicates that the magnitude of Eric's score was closer to their grades state record
What is the magnitude of a value?The magnitude of a value is the value itself, indicating the distance of the number from zero.
Alex is an eight grader
Eric is a seventh grader
The distance Alex jumped = 39.75 feet
The distance Eric jumped = 37 feet 11 inches
The eight grade record = 42.25 feet
The seventh grade record = 39 feet 3 inches
Each athlete distance jumped is compared with the record for the grade at which they jumped
The deviation of the distance jumped from the record scores are;
Alex's difference between distance jumped and the record = 39.75 - 42.25 = -2.5
The difference between the distance Eric jumped and the record = 37 feet + 11 inches - (39 feet + 3 inches) = -(1 feet + 4 inches)
-(1 feet + 4 inches) = -1.[tex]\overline 3[/tex] inches
The magnitude of the difference between the distance Eric jumped and the state record is smaller, therefore, Eric was closer to the state record
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Answer: I can confirm that Eric is closer!
Step-by-step explanation:
a factory bottles 360 bottles of juice in 5 minutes find the factory’s into rate bottles per minute
The factory produces 72 bottles of juice per minute.
What is the rate?
A rate is a special ratio in which the two terms are in different units. If a 12-ounce can of corn costs $69, the rate is $69 for 12 ounces. This is not a proportion of two comparable units, such as shirts. This is a proportion of two dissimilar units: cents and ounces.
To find the factory's production rate in bottles per minute, we need to divide the number of bottles produced by the time it took to produce them. In this case, the factory produced 360 bottles in 5 minutes, so the production rate is:
360 bottles / 5 minutes = 72 bottles/minute
This means that the factory produces 72 bottles of juice per minute.
Hence, the factory produces 72 bottles of juice per minute.
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Sample Space = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 2, 3, 4}
B={1, 3, 5, 7, 9}
Find P(A and B)
The value of P(A and B) is 1/5.
What is Sample Space?
The set of all potential outcomes or results of an experiment or random trial is referred to as the sample space in probability theory. The sample points, or potential ordered outcomes, are listed as elements in the set notation used to represent a sample space.
Here, we have
Given
Sample Space = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 2, 3, 4}
B={1, 3, 5, 7, 9}
We have to find P(A and B).
First, we will find A and B i.e A∩B
A∩B = {1,3}
Now, we will find P(A and B).
P(A and B) = n(A∩B)/n(S)
P(A and B) = 2/10
P(A and B) = 1/5
Hence, the value of P(A and B) is 1/5.
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The equation of line s is y=–4x–5/3. Line t includes the point (–3,3) and is parallel to line s. What is the equation of line t?
Answer:
write the equation in slope intercept form. Write the numbers in the equation as simplified proper fraction improper fraction or integer
The equation of the parallel line t is y = -4x - 9.
The equation of line s is given as
y = -4x - 5/3
Also, from the question, the point on line t is given as Point = (-3, 3)
The equation of a line can be represented as
y = m x + c-------(1)
Where m represents the slope
c is the constant value
By comparing the equations, we have the following
m = -4
This means that the slope of y = -4x - 5/3 is -4
The slopes of parallel lines are equal
This means that the slope of the line t is -4
The equation of the parallel line is then calculated as:
y = m(x - x₁) +y₁
Where m = -4
(x₁, y₁) = (-3, 3)
Now, we should substitute the known values in the above equation(1)
y = -4(x + 3) + 3
By Evaluating we get
y = -4x - 12 + 3
y = -4x - 9
Hence, the parallel line has an equation of y = -4x - 9.
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What is the answer i need answers now I'm am going to fail
Answer:
5f + 4s
Step-by-step explanation:
Third option
What is the sampling method that involves taking a random selection of people from a defined population?.
Simple random sampling is a sort of probability sampling in which a selection of participants is randomly chosen from a population by the researcher.
What is Probability?The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.
The probability of an event can be calculated using the following formula.
Probability(Event) = Positive Results/Total Results = x/n
In order to better grasp probability, let's look at a straightforward application.
Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.
There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.
Hence, In probability sampling, a sample is chosen from a population based on the randomization principle, also known as chance or random selection.
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Consider the probability that greater than 90 out of 149 software users will not call technical support. Assume the probability that a given software user will not call technical support is 56%. Approximate the probability using the normal distribution. Round your answer to four decimal places.
Answer:
0.1220
Step-by-step explanation:
You want the probability that greater than 90 out of 149 software users will not call tech support, given that the probability a given user will not call is 56%. You want the value using the normal approximation to the binomial distribution.
Normal approximationFor a sample size of n, and probability p of "success", the normal approximation to the binomial distribution can be used if ...
min(pn, (1-p)n) > 5
Here, that is ...
min(0.56·149, 0.44·149) > 5
65.6 > 5 . . . . . . . . true, the normal approximation is appropriate
Then the parameters of the normal distribution are ...
µ = pn = 0.56·149 = 83.44
σ = √((1-p)µ) = √(0.44·83.44) ≈ 6.0592
Continuity correction factorThe probability that X = N will occur can be considered to be ...
P(N -0.5 < X < N +0.5)
Then the probability that X > N will be modeled using the normal distribution as ...
P(X > N +0.5)
For this problem, we want ...
P(X > 90.5) . . . . using the normal distribution with µ = 83.44, σ = 6.0592
The attached calculator shows that value to be ...
P(>90) ≈ 0.1220 . . . . . . rounded to 4 decimal places
__
Additional comment
A probability calculator says the actual binomial distribution result for this problem is 0.1217.
Wes made 8 cups of fresh peanut butter and divided equally among 6 jars.- How much
peanut butter went in each container?
Answer:
Step-by-step explanation:
1 1/3 cups peanut butter
proof:
1 1/3 +1 1/3+1 1/3+1 1/3+1 1/3+1 1/3 = 8 cups
Jamie is an analyst at an education technology company. She gathered data on the results of a certain type of question. Of the 2,000 re
she looked at, 1,092 responded correctly.
What equation could Jamie use to calculate the margin of error at a 90% confidence interval?
0. 454
2. 58
1,092
1. 96
2,000
0. 546
1. 65
(1-1
ME=
Reset
Next
Next
The 90% confidence interval's margin of error is 0.0183, and its success probability is 0.546.
What is margin of error?The term "margin of error" refers to the probability or "chances of error" when selecting or computing a sample in a survey.
Jamie works as an analyst for a provider of educational technologies. She gathered information on the outcomes of a particular kind of query. 1,092 of the 2,000 replies she examined were accurate.
Here,
Number of samples, N=2000
Probability of responding correctly,
=1092/2000
=0.546
Z-score at 90% confidence level,
=1.645
Margin of Error ME,
=z*√(p*(1-p)/N)
=1.645*√(0.546*(1-0.546)/2000)
=1.645*√(0.546*0.454)/2000
=1.645*√(0.248/2000)
=1.645*√0.000124
=1.645*0.011
=0.0180
With a success rate of 0.546 percent, the margin of error for the 90% confidence interval is 0.0183.
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Plssss help What is the solution to the system? 2x-2y=2, y=-5x+14
Answer:
x=2.5, 5/2
y=1.5, 3/2
Step-by-step explanation:
2x-2(-5x+14)=2
2x+10x-28=2
12x=30
x=2.5
y=-5(2.5)+14
y=-12.5+14
y=1.5
Question regarding Modulus attached below.
Answer:
x=4/3, 8/3
Step-by-step explanation:
We will solve this in two steps, one where the right hand side is 2, one where it is -2. This is because the equation is satisfied either way when [tex]|6-3x|[/tex] is equal to either of those values.
Let's start with 2. We have [tex]6-3x=2[/tex]. Subtracting 6 from both sides and then dividing by 3 gives us that x = 4/3. This is the first value.
Now, we solve for when it equals -2. We have [tex]6-3x=-2[/tex]. Subtracting 6 from both sides and then dividing by 3 gives us that x = 8/3. This is the second value.
Feel free to contact me with any questions about my answer. I hope this helps!