Yvette maps out several locations in her town, with distances and angles between them. Two triangles are formed within the map.
To conclude that these triangles are congruent by SAS Congruence Postulate, what must the distance between the school and the park be
Answers
To be both triangles to be congruent the distance between the school and the park be 1.1 miles.
What is congruence?If two figures are exactly the same in sense of their length side all things then they will be congruent.
If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent or to be in the relation of congruence.
As per the given two triangles,
The side 2.7 miles is the common side.
The angle is 52 degrees in both triangles same.
To be congruent any one side must be the same by the SAS rule.
Thus, the school-to-park corresponding side is school-to-store.
school to park = 1.1 miles
Hence "To be both triangles to be congruent the distance between the school and the park be 1.1 miles".
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Related Questions
9. Use the figure shown to identify each.
a. Vertical angles
b. Adjacent angles
c. Linear pairs
d. Supplementary angles
e. Complementary angles
Answers
The angles in the given figure are:
a. Vertical angles: angle 3 and angle 5.
b. Adjacent angles: angle 1, angle 2, angle 3, angle 4, and angle 5.
c. Linear pairs: angle 3 and angle 4, angle 4 and angle 5.
d. Supplementary angles: angle 4 and angle 5.
e. Complementary angles: angle 1 and angle 2.
We are given a figure and we need to identify the angle.
Let us identify the angle:
a. Vertical angles:
Each of the pairs of opposite angles is made by two intersecting lines.
In the given figure,
angle 3 and angle 5 are vertical angles.
b. Adjacent angles:
In the given figure,
angle 1, angle 2, angle 3, angle 4, and angle 5.
c. Linear pairs:
The sum of the two angles should be 180 degrees.
In the given figure,
angle 3 and angle 4, angle 4 and angle 5.
d. Supplementary angles:
The sum of the two angles should be 180 degrees.
In the given figure,
angle 4 and angle 5.
e. Complementary angles:
The sum of the two angles should be 90 degrees.
In the given figure,
angle 1 and angle 2.
Thus, the angles in the given figure are:
a. Vertical angles: angle 3 and angle 5.
b. Adjacent angles: angle 1, angle 2, angle 3, angle 4, and angle 5.
c. Linear pairs: angle 3 and angle 4, angle 4 and angle 5.
d. Supplementary angles: angle 4 and angle 5.
e. Complementary angles: angle 1 and angle 2.
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Beginning with the equation 27x=54, write the new equation produced by dividing both sides by 9
Answers
Answer:
3x=6
Step-by-step explanation:
27/9=3, 54/9=6 so answer is 3x = 6
The probability that an employee will be late to work at a large corporation is 0.21. What is the probability on a given day that in a department of 5 employees at least 3 are late ?
Answers
Given:
Number of employees are 5.
Probability that an employee will be late to work at a large corporation is 0.21.
The given data follows binomial distribution,
[tex]\begin{gathered} X\text{ \textasciitilde{}B(n,p,q)} \\ n=5 \\ p=0.21 \\ q=1-p=1-0.21=0.79 \\ P(X=x)=^nC_xp^xq^{n-x} \end{gathered}[/tex]The probability that at least 3 employees are late is given as,
[tex]\begin{gathered} P(X\ge3)=P(X=3)+P(X=4_{})+P(X=5) \\ P(X\ge3)=^5C_3(0.21)^3(0.79)^{5-3}+^5C_4(0.21)^4(0.79)^{5-4}+^5C_5(0.21)^5(0.79)^{5-5} \\ P(X\ge3)=0.0578+0.0077+0.0004 \\ P(X\ge3)=0.0659 \end{gathered}[/tex]Answer: The probability that in a department of 5 employees at least 3 are late is 0.0659.
A contractor is pouring a rectangular concrete slab with dimensions of 16 feet by 30 feet. To ensure that the sides of the slab form 90° angles, how many feet should each diagonal measure?.
Answers
If each sides of the slab form 90° angles, The number of feet that
each diagonal measure is 34 feet.
How to find the diagonal feet?
Using Pythagoreans theorem formula to find the diagonal feet
D² =L² + W²
Where:
D = Diagonal
L= Length = 16 feet
W = Width = 30
Let plug in the formula
D² = 16² + 30²
D² = 256 + 900
D=√1156
D= 34 feet
Therefore the diagonal measure 34feet
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Figure T is the result of a transformation on Figure S. Which transformation would accomplish this? 6 -4 -3 2 3 Figure S Figure T -3 -4 -5
Answers
Let:
[tex]\begin{gathered} A=(1,-1) \\ A^{\prime}=(3,-2) \\ A\to(x+a,y+b)\to A^{\prime} \\ so\colon \\ 1+a=3 \\ a=3-1=2 \\ ---- \\ -1+b=-2 \\ b=-2+1=-1 \\ so\colon \\ A\to(x+2,y-1)\to A^{\prime} \end{gathered}[/tex]Therefore, the transformation T is:
A translation 2 units right and 1 unit down
-6.75 Natural, whole, integer, rational, irracional, real,
Answers
-6.75 is a rational number.
Let us understand about natural, whole, integer, rational, and irrational numbers one by one.
Natural number:
Natural numbers are numbers that start from 1 and end at infinity. These are non-negative numbers.
Whole number:
Whole numbers are numbers that start from 0 and end at infinity.
We can also natural numbers including 0 is known as whole numbers.
These are non-negative numbers.
Integer:
An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.
Rational number:
A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p, and a non-zero denominator q.
Also, the decimal representation of the rational number is terminating and recurring.
Irrational number:
An irrational number is a number that can not be expressed as the quotient or fraction p/q of two integers, a numerator p, and a non-zero denominator q.
Also, the decimal representation of the irrational number is non-terminating and non-recurring.
The given number is -6.75.
The decimal form is terminating.
So, it is a rational number.
Thus, -6.75 is a rational number.
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Help the question is attached
Answers
The correct option will be A that is t=(A-P)/Pr by the simplification of equation, "an equation is a mathematical statement that shows that two mathematical expressions are equal ".
What is equation?In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. In mathematics, an equation is a relationship of equality between two expressions written on both sides of the equal to sign. 3y = 16 is an example of an equation. Some examples of important equations are:
Linear equationsQuadratic equationsCubic equationQuadratic equationsDifferential equationsParametric equationsHere,
A=P+Prt
A-P=Prt
t=(A-P)/Pr
The answer is A, which is t=(A-P)/Pr using the equation's simplified form. An equation is a mathematical statement that demonstrates the equality of two mathematical expressions.
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A supply company manufactures copy machines. The unit cost C (the cost in dollars to make each copy machine) depends on the number of machines made. If x machines are made in the unit cost is given by the function C(x)=x^2-520x+79,797. What is the minimum unit cost? Do not round your answer.
Answers
Answer:
The minimum unit cost is $12,197.
Explanation:
The cost function is given below:
[tex]C\mleft(x\mright)=x^2-520x+79,797[/tex]To find the minimum unit cost, first, find the derivative of C(x).
[tex]C^{\prime}(x)=2x-520[/tex]Next, set the derivative equal to 0 and solve for x.
[tex]\begin{gathered} 2x-520=0 \\ 2x=520 \\ x=520\div2 \\ x=260 \end{gathered}[/tex]Finally, substitute x=260 into C(x) to find the minimum cost.
[tex]\begin{gathered} C\mleft(x\mright)=x^2-520x+79,797 \\ \implies C(260)=(260)^2-520(260)+79,797 \\ =67600-135,200+79,797 \\ =12,197 \end{gathered}[/tex]The minimum unit cost is $12,197.
Answer the questions below.(a) The perimeter of a rectangular parking lot is 314 m.If the width of the parking lot is 71 m, what is its length?Length of the parking lot: 0 m(b) The area of a rectangular pool is 8075 m.If the length of the pool is 95 m, what is its width?Width of the pool: m
Answers
We have to use the perimeter formula for rectangles
[tex]P=2(w+l)[/tex]Where P = 314 m and w = 71 m.
[tex]\begin{gathered} 314=2(71+l) \\ \frac{314}{2}=71+l \\ 71+l=157 \\ l=157-71 \\ l=86 \end{gathered}[/tex]Hence, the length is 86 meters.Find (f + g)(x), if f(x) = - 5x2 + 6 and g(x) = x2 - 6.4x2- 6x2 + 12- 4x2- 6x2 - 12
Answers
Given the functions:
[tex]\begin{gathered} f(x)=-5x^2+6 \\ g(x)=x^2-6 \end{gathered}[/tex][tex]\begin{gathered} (f+g)(x)=f(x)+g(x) \\ (f+g)(x)=(-5x^2+6)+(x^2-6)=-5x^2+x^2+6-6 \\ (f+g)(x)=-4x^2+0=-4x^2 \end{gathered}[/tex]The answer is: C. -4x^2.
5#Consider the following random sample of diameter measurements (in inches) of 12 softballs.4.72, 4.74, 4.83, 4.75, 4.73, 4.87, 4.69, 4.7, 4.76, 4.7, 4.79, 4.76Send data to calculatorIf we assume that the diameter measurements are normally distributed, find a 90% confidence interval for the mean diameter of a softball. Give the lower limit and upper limit of the 90% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to two decimal places. (If necessary, consult a list of formulas.)Lower limit:??Upper limit:??
Answers
ANSWER:
Lower limit: 4.73
Upper limit: 4.78
STEP-BY-STEP EXPLANATION:
Given the following data set:
[tex]4.72,4.74,4.83,4.75,4.73,4.87,4.69,4.7,4.76,4.7,4.79,4.76[/tex]We calculate the mean and standard deviation:
[tex]\begin{gathered} \mu=\frac{4.72+4.74+4.83+4.75+4.73+4.87+4.69+4.7+4.76+4.7+4.79+4.76}{12}=\frac{57.04}{12}=4.753 \\ \\ \sigma=\sqrt{\frac{\lparen4.72-4.753^2+\left(4.74-4.753\right)^2+\lparen4.83-4.753)^2+\left(4.75-4.753\right)^2+\left(4.73-4.753\right)^2+\lparen4.87-4.753)^2+\left(4.69-4.753\right)^2+\lparen4.7-4.753)^2+\left(4.76-4.753\right)^2+\left(4.7-4.753\right)^2+\left(4.79-4.753\right)^2+\left(4.76-4.753\right)^2}{12-1}} \\ \\ \sigma=0.054 \end{gathered}[/tex]The critical limit of 90% confidence interval is 1.645
We can determine the limits as follows:
[tex]\begin{gathered} \text{ Lower limit: }\mu-Z\cdot\frac{\sigma}{\sqrt{n}}=4.753-1.645\cdot\frac{0.054}{\sqrt{12}}=4.727\cong4.73 \\ \\ \text{ Upper limit:: }\mu+Z\cdot\frac{\sigma}{\sqrt{n}}=4.753+1.645\cdot\frac{0.054}{\sqrt{12}}=4.778\cong4.78 \end{gathered}[/tex]A restaurant uses 8 ¼ pounds of flour to make 6 cakes. Beatriz wants to use the same recipe. How many pounds of flour does she need for one cake?
Answers
If A restaurant uses [tex]8\frac{1}{4}[/tex] pounds of flour to make 6 cakes. Beatriz wants to use the same recipe, then [tex]1\frac{3}{8}[/tex] pounds of flour is used for one cake
What is Division?A division is a process of splitting a specific amount into equal parts.
Given,
A restaurant uses [tex]8\frac{1}{4}[/tex] pounds of flour to make 6 cakes
We need to find how many pounds of flour does she need for one cake
To find this we just need to divide [tex]8\frac{1}{4}[/tex] pounds by 6.
[tex]8\frac{1}{4}[/tex] is 33/4
33/4/6
33/24
11/8
[tex]1\frac{3}{8}[/tex] pounds
Hence [tex]1\frac{3}{8}[/tex] pounds of flour is used for one cake
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An isosceles trapezoid has perimeter of 70. Each of the congruent nonparallel sides has length 13, and the height of the trapezoid is 12. How long is the longest side?
Answers
The length of the longest side is 27 units, in the isosceles trapezoid.
What is isosceles trapezoid?
A four-sided shape called a trapezoid has two parallel lines on each side (normally the top and bottom sides). A trapezoid that has equal-length non-parallel sides (the legs) is said to be isosceles. Considering everything mentioned before, we may start learning how to calculate an isosceles trapezoid's perimeter.
Given, the congruent nonparallel sides has length 13.
he height of the trapezoid is 12.
the extra length of the larger side will be 2*x, as it will be extra portion in both side.
So x² = 13²-12²
x² = 169-144 = 25
x = √25 = 5
So the lentgh of the larger side is 10 unit larger than smaller side.
The perimer of the isosceles trapezoid will be P = sum of all sides
P = 2*13 + L + L+10
⇒70 = 26+10 +2L
⇒2L = 70 - 36
⇒2L = 34
⇒L = 17
The length of the larger side will be 17+10 = 27 units.
Hence the length of the longest side is 27 units.
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how long will it take for the population to reach 5656 fish, according to this model?
Answers
Question:
Solution:
The population growth is given by the following equation:
[tex]P(t)=(707)2^{\frac{t}{3}}[/tex]where P represents the number of individuals and t represents the number of years from the time of introduction. Now, if we have a population of 5656 fish, then the above equation becomes:
[tex]5656=(707)2^{\frac{t}{3}}[/tex]this is equivalent to:
[tex]2^{\frac{t}{3}}\text{ = }\frac{5656}{707}[/tex]this is equivalent to:
[tex]2^{\frac{t}{3}}\text{ = }8[/tex]this is equivalent to:
[tex](2^t)^{\frac{1}{3}}\text{ = }8[/tex]now, the inverse function of the root function is the exponential function. So that, we can apply the exponential function to the previous equation:
[tex]((2^t)^{\frac{1}{3}})^3\text{ = }8^3[/tex]this is equivalent to:
[tex](2^t)^{\frac{3}{3}}^{}\text{ = }512[/tex]this is equivalent to:
[tex]2^t\text{ = }512[/tex]now, we can apply the properties of the logarithms to the previous equation:
[tex]\log _2(2^t)\text{ = }log_2(512)[/tex]this is equivalent to:
[tex]t=log_2(512)\text{ = 9}[/tex]we can conclude that the correct answer is:
9 years
Please assist me, oh great smart people of the internet!
Answers
The value of x in (5 + 2x)/3 < (2x + 2)/4 is x < - 7.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, Inequality is (5 + 2x)/3 < (2x + 2)/4.
Now, (5 + 2x)/3 - (2x + 2)/4 < 0.
{4(5 + 2x) - 3(2x + 2)}/12 < 0.
{20 + 8x - 6x - 6}/12 < 0.
(2x + 14)/12 < 0.
2x + 14 < 0.
x + 7 < 0.
x < - 7.
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A skating rink manager finds that revenue R based on an hourly fee F
for skating is represented by the function R = -480F² + 3120F.
What hourly fee will produce maximum revenues?
Answers
The hourly fees of $3.25 will produce the maximum value of revenue in the Skating rink.
Given function of the form:
R = -480F² + 3120F
Here R is the revenue and F is the hourly fees.
Now we will differentiate with respect to F
Hence.
[tex]\frac{dR}{dF} = -960F + 3120[/tex]
Now to find the maximum value we have to find the value of F for which [tex]\frac{dR}{dF}[/tex] is zero.
hence :
-960F+3120 = 0
or, F=3.25
Hence the value of F is 3.25 for which the revenue will be maximum.
Maxima and minima, the corresponding plurals of lower and upper bound of a function, are used in mathematical analysis to refer to the highest and lowest value of such a function, whether it be within or a defined range, the local the relative extrema, or throughout the entire domain.
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1. Michelle used a standard deck of 52 cards and selected a card at random. Afterrecording the suit of the card she picked, she then replaced the card.SultOutcomeSpades 9Hearts11Clubs7Diamonds3Part A: Determine the empirical probability of selecting a heart.Part B: Determine the theoretical probability of selecting a heart.Part C: Determine the empirical probability of selecting a club or diamond.Part D: Determine the theoretical probability of selecting a club or diamond.
Answers
The card deck is a standard deck of 52 cards, with 13 cards in each suit.
For the experiment carried out by Michelle, we have the following information:
n(Spades) = 9
n(Hearts) = 11
n(Clubs) = 7
n(Diamonds) = 3
The total number of times she performed the experiment is
[tex]n(\text{Total) = 9+11+7+3 = 30}[/tex]The empirical probability will make use of the experimental results, while the theoretical probability will make use of the total possibilities.
PART A: Empirical Probability of selecting a heart.
Probability is calculated by
[tex]P(\text{outcome) = }\frac{n(outcome)}{n(total)}[/tex]Therefore, the probability is calculated as
[tex]P(\text{heart) = }\frac{11}{30}[/tex]PART B: Theoretical probability of selecting a heart.
This is calculated by
[tex]\begin{gathered} P(\text{heart) = }\frac{13}{52} \\ P(\text{heart) = }\frac{1}{4} \end{gathered}[/tex]PART C: Empirical probability of selecting a club or diamond.
To calculate the probability for two outcomes, A or B, the probability can be calculated by
[tex]P(A\text{ or B) = P(A) + P(B)}[/tex]Therefore, we will find the probability of getting a club and then a diamond.
[tex]P(\text{heart) = }\frac{11}{30}[/tex][tex]P(\text{diamond) = }\frac{3}{30}=\frac{1}{10}[/tex]Therefore, the probability of selecting a club or a diamond is
[tex]\begin{gathered} P(\text{heart or diamond) = }\frac{11}{30}+\frac{1}{10} \\ P(\text{heart or diamond) = }\frac{7}{15} \end{gathered}[/tex]PART D: Theoretical probability of selecting a club or a diamond
We will find the probability of getting a club and then a diamond.
[tex]P(\text{club) = }\frac{13}{52}=\frac{1}{4}[/tex][tex]P(\text{diamond) = }\frac{13}{52}=\frac{1}{4}[/tex]Therefore, the probability of selecting a club or a diamond is
[tex]\begin{gathered} P(\text{heart or diamond) = }\frac{1}{4}+\frac{1}{4} \\ P(\text{heart or diamond) = }\frac{1}{2} \end{gathered}[/tex]points (-2,1) and (3,y) have a slope of -3. find the y coordinate of the point
Answers
y coordinate of the point is -14
Explanation:Slope = change in y/change in x
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ m\text{ = -3} \end{gathered}[/tex]Since m is negative, it means the slope is negative.
[tex]\begin{gathered} It\text{ also means the 2nd y value will be smaller than the 1st y value to get negative slope} \\ x_1=-2,y_1=1,x_2=3,y_2\text{ = y} \\ m\text{ = }\frac{y-1}{3-(-2)} \end{gathered}[/tex][tex]\begin{gathered} -3\text{ = }\frac{y-1}{3+2} \\ -3\text{ = }\frac{y-1}{5} \\ -3(5)\text{ = y - 1} \\ -15\text{ = y - 1} \\ \end{gathered}[/tex][tex]\begin{gathered} -15\text{ + 1 = y} \\ y\text{ = -14} \\ y\text{ coordinate of the point is -14} \end{gathered}[/tex]Kehlani went into a movie theater and bought 6 bags of popcorn and 8 drinks, costing a total of $76. Madelyn went into the same movie theater and bought 7 bags of popcorn and 4 drinks, costing a total of $62. Determine the price of each bag of popcorn and the price of each drink.
Answers
The price of each bag of popcorn and the price of each drink are $6 and $5 respectively.
What is equation?Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.
Given:
The no of popcorn bags bought by Kehlani = 6,
The no of popcorn bags bought by Madelyn = 7,
The no of drinks bought by Kehlani = 8,
The no of drinks bought by Madelyn = 4,
The costing by Kehlani = $76,
The costing by Madelyn = $62,
Let the price of the popcorn bag is x and the price of the drink is y, then,
According to the question statement,
6x + 8y = 76 and 7x + 4y = 62,
Solve the equation by the elimination method,
x = 6 and y = 5
Therefore, the price of each bag of popcorn and the price of each drink are $6 and $5 respectively.
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(24x3 − 14x2 + 20x + 6) ÷ (4x2 − 3x + 5) = Q +
R
4x2 − 3x + 5
Q =
R =
Answers
Answer:
Step-by-step explanation:
Dividend = 24x³ - 14x² + 20x + 6
What is the solution to the equation 7x−4=3x−8 , given the replacement set {−3, −1, 1} ?
A. -3
B. -1
C. 1
D. I don't know
Please answer fast!
I will give 85 points to whoever answers this question first, and I will also give whoever answers first brainliest.
Answers
Answer: B
Step-by-step explanation:
7x-4=3x-8
Combine like terms
7x-3x=4-8
Simplify
4x=-4
Divide
x=-1
Which of these pieces of data about a package delivered by the post office is considered categorical data?A. Surface areaB. WeightC. Volume D. Dropoff location
Answers
Answer
D. Dropoff location
Step-by-step explanation
Quantitative variables are any variables where the data represent amounts (e.g. surface area, weight, or volume of a package). Categorical variables are any variables where the data represent groups (for example classifications like cities or brands).
What is the length of the segment shown on the graph? (Label your answer "units".)
Answers
Using the above graph, we can calculate that the segment has a length of 8 units.
What is the definition of a line segment?A line segment in geometry has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in any direction.Describe a line segment example.In real life, a line segment may be a stick, a pencil, or a ruler. The sun's beams are an illustration of a segmentThe graph shows the segment and dimensions given at the end of the segment are -4 and 4.
Thus we can say that, the first half of the segment is having the length 4 units and the other half also has the same length of 4 units.
By, adding both these lengths we get,
4 + 4 = 8 units
Therefore, the length of the segment is 8 units which is computed using the given graph.
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How do I figure out what graph(s) is linear or exponential? can someone explain how to do this for me?
Answers
Answer:
Linear functions are graphed as straight lines while exponential functions are curved. Linear functions are typically in the form y = mx + b, which is used to discover the slope, or simply the change in y divided by the change in x, while exponential functions are typically in the form y = (1 + r) x.
Step-by-step explanation:
Tanya is printing a report. There are 100 sheets of paper in the printer, and the number of sheets p left after
t minutes of printing is given by the function p(t) = -8t + 100.
Part A
How long would it take the printer to use all 100 sheets of paper? Explain how you found your answer.
Answers
It will take 12.5 minutes by the printer to use all 100 sheets of paper as the function is p(t) = -8t + 100 where p is the number of sheets left after t minutes of printing.
What is function?A mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). The property that every input is related to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets. Four broad categories can be used to classify different types of functions. dependent upon element Function is a one-to-one relationship, a many-to-one relationship, onto function, one-to-one and into function.
Here,
p(t)=-8t+100
Tanya is printing a report. There are 100 sheets of paper in the printer, and the number of sheets of paper p left after t minutes of printing is given by the function .When all the 100 sheets printed , then the number of sheets will left to print =0.
Substitute p(t)=0 in the given function, to find the value of t,
0=-8t+100
8t=100
t=12.5 minutes
The function is p(t) = -8t + 100, where p is the number of sheets left after t minutes of printing, and it will take the printer 12.5 minutes to use all 100 sheets of paper.
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PLEASE HELP ME OUT What is x^2 - 4
Answers
Answer: (x-2)(x+2) is the solution
Step-by-step explanation:
Use the sum-product pattern
Common factor from the two pairs
Rewrite in factored form
Answer:
(x-2)(x+2)
Step-by-step explanation:
Solve for x:
2.50+1.50x=3.25+1.25x
Answers
Answer:
x = 3
Step-by-step explanation:
Multiply both sides by 100
2.5 · 100 + 1.5x · 100 = 3.25 · 100 + 1.25x · 100
Refine:
250 + 150x - 250 = 325 + 125x - 250
Simplify:
150x = 125x + 75
Subtract 125x from both sides:
150x - 125x = 125x + 75 - 125x
simplify:
25x = 75
Now all you have to do is Divide both sides by 25:
[tex]\frac{25x}{25}[/tex] = [tex]\frac{75}{25}[/tex]
Now Finally the last part Now just Simplify so therefore the answer is
x = 3
you are planning a survey of starting salaries for recent business majors. in the 2018 survey by the national association of colleges and employers, the average starting salary was reported to be $56,720. if you assume that the standard deviation is $11,500, what sample size do you need to have a margin of error equal to $1,000 with 95% confidence?
Answers
The sample size you need to have a margin of error equal to $1,000 with 95% confidence is; 508
How to find the sample size?Formula for margin of error is given by the formula;
E = z(σ/√n)
where;
z is z-score at significance level
σ is standard deviation
n is sample size
We are given;
σ = $11500
z at significance level of 0.05 is 1.96
margin of error; E = $1000
Thus;
1000 = 1.96(11500/√n)
√n = (1.96 * 11500/1000)
√n = 22.54
n = 22.54²
n ≈ 508
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x + 6=13 show the steps
Answers
Solve the quadratic equation by using the quadratic formula. 3x^2-5x+1=4 Enter your solutions below from smallest to largest. If a solution is repeated type that answer for both values of x. If your answer is not an integer then type it as a decimal rounded to the nearest hundredth.
Answers
Answer:
x = -0.47, x = 2.14
Step-by-step explanation:
Quadratic formula is my favorite!!
Let's first take that four over to the other side
Subtract 4 from both sides
3x^2-5x-3
a = 3
b = -5
c = -3
Remember quadratic formula: [tex]x=\frac{-b(+-)\sqrt{b^2-4ac} }{2a}[/tex]
IGNORE THE A BEFORE THE ±
Plug in our a, b, and c values: [tex]x=\frac{-(-5)±\sqrt{5^2-4(3)(-3)} }{2(3)}[/tex]
Simplify: [tex]x=\frac{5±\sqrt{25+36} }{6}[/tex]
Simplify some more: [tex]x=\frac{5±\sqrt{61} }{6}[/tex]
Solve:
x ≈ -0.47
x ≈ 2.14