For the data in the table, does y vary directly with x? If it does write an equation for the direct variation. x 2 6 10 y 5 15 25
A business woman invests $38,000 into two accounts: one that returns 3.5% annual interest and one that returns 6.5% annual interest. After 1 year, she earns $1960. How much did she invest in each account?
$23,000 in the 3.5% interest account, $15,000 in the 6.5% interest account.
$26,000 in the 3.5% interest account, $12,000 in the 6.5% interest account.
$12,000 in the 3.5% interest account, $26,000 in the 6.5% interest account.
$17,000 in the 3.5% interest account, $21,000 in the 6.5% interest account.
Final answer:
The business woman invested $17,000 in the 3.5% interest account and $21,000 in the 6.5% interest account.
Explanation:
To find how much she invested in each account:
Let x be the amount invested at 3.5% interest and y be the amount at 6.5%.
We can set up a system of equations like this: x + y = $38,000 and 0.035x + 0.065y = $1,960.
Solving this system, we get x = $17,000 and y = $21,000.
Therefore, investment is $17,000 in the 3.5% interest account, $21,000 in the 6.5% interest account
Jan is saving for a skateboard. She has saved $30 already, which is 20% of the total price. How much does the skateboard cost
James believes the honor roll students at his school have an unfair advantage in being assigned to the math class they request. He asked 500 students at his school the following questions: "Are you on the honor roll?" and "Did you get the math class you requested?" The results are shown in the table below:
Honor roll Not on honor roll Total
Received math class requested 315 64 379
Did not get math class requested 41 80 121
Total 356 144 500
Help James determine if all students at his school have an equal opportunity to get the math class they requested. Show your work and explain your process for determining the fairness of the class assignment process.
If Tim and Terry started to run in opposite directions with the speeds of 90 feet per minute and 11 feet per minute respectively, how far away from each other will they be in 18 minutes?
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To find the distance between Tim and Terry after 18 minutes, you can calculate the distance each has traveled based on their speed and time elapsed. Then subtract their distances to find the total distance between them.
To determine the distance between Tim and Terry after 18 minutes, you can add up the distances each has traveled according to their speeds and time elapsed. Tim covers 90 feet/minute, so in 18 minutes, he would have traveled 90 * 18 = 1620 feet. Terry covers 11 feet/minute, so in 18 minutes, he would have traveled 11 * 18 = 198 feet.
Calculating the total distance between them:
Distance = |1620 - 198| = 1422 feet
Jermiah bought 3 sanwiches for lunch if each sandwich cost $4 how much did Jeremiah spend in all
find the area of each triangle 10inches 9inches
due to the same law, persons earning $500,000 per year had lower taxes removed from their paychecks on the first $106,800 they earned, saving them 2% of this portion of their salary. The same persons also received $14,250 more on their federal tax return. Fill in the blanks to complete the statement below. A person earning $500,000 a year received $______ more or______ % more of their income. Round to the nearest dollar and to the nearest tenth of a percent.
Final answer:
A person earning $500,000 per year received an additional $16,386 or 3.3% more of their income due to tax changes.
Explanation:
To ascertain how much more a person earning $500,000 per year received due to tax changes, we need to calculate the savings from the first $106,800 at a 2% reduction, in addition to the increased federal tax return of $14,250.
Firstly, we calculate 2% of $106,800:
0.02 × $106,800 = $2,136
Now, we add this to the additional amount received from the tax return:
$2,136 + $14,250 = $16,386
Therefore, a person earning $500,000 per year has received an additional $16,386. To find the percentage this additional amount represents of their income, we perform the following calculation:
($16,386 / $500,000) × 100 = 3.277%
Rounded to the nearest tenth of a percent, it is 3.3%.
The statement completed would be: A person earning $500,000 a year received $16,386 more or 3.3% more of their income.
At the end of each year, how much money would you earn in interest if you invested $3,500 and earned 4.5% simple interest?
A First City Bank accepted a $3,500, 5%, 120-day note dated August 8 from a Capstone Company in settlement of a past bill. On October 11, First City discounted the note at Park Bank at 6%.
a. What is the note’s maturity value? (Use 360 days a year. Do not round intermediate calculations. Round your final answer to the nearest cent.)
b. What is the discount period?
c. What is the bank discount? (Use 360 days a year. Do not round intermediate calculations. Round your final answer to the nearest cent.)
d.
What proceeds does First City receive? (Use 360 days a year. Do not round intermediate calculations. Round your final answer to the nearest cent.)
calculate the length of a scarf with sections if each section is 1/2 foot long
Jessica is making a repeating pattern following the rule “triangle square circle what will be the 50th shape in the pattern?
The 50th shape in the repeating sequence of shapes (triangle, square, circle) is a square. This conclusion is reached by dividing 50 by the 3 shapes in the sequence and noting that the remainder indicates the position in the sequence.
Explanation:The problem presented is one of patterns and sequences, a common topic explored in middle school mathematics. The repeating pattern here consists of three shapes: a triangle, a square, and a circle. This sequence of three shapes continues indefinitely.
To find the 50th shape in the sequence, divide 50 by 3. You'll get 16 remainder 2. This indicates that after 16 complete cycles of the pattern (each consisting of a triangle, square, or circle), the 50th shape is the 2nd shape in the next cycle - the square. Hence the 50th shape according to Jessica's rule is a square.
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The 50th shape in the repeating pattern of Triangle, Square, Circle is a Square.
To find the 50th shape, we need to understand the cyclical nature of this pattern, which repeats every 3 shapes.
Step-by-Step Solution:
The pattern repeats every 3 shapes: Triangle (1), Square (2), Circle (3).To find the position of the 50th shape within this cycle, we calculate the remainder of 50 divided by 3:Therefore, the 50th shape is a Square.
TOAD is a quadrilateral with vertices (9, 10), (18, 10), (14, 5), and (5, 5), respectively. The diagonals intersect at Point S.
Use the given information to:
a) classify the quadrilateral as a parallelogram, square, rectangle or rhombus
b) determine the intersection of the diagonals
c) use the distance formula to prove that the diagonals are bisectors of each other
⇒Plotting the Quadrilateral on two Dimensional Plane
And finding the diagonal of Quadrilateral bisect each other.
If you will look at the Quadrilateral, none of the interior angle is of 90°, so it can't be Square or Rectangle.
Finding the length of two Adjacent Sides
[tex]TO=\sqrt{(18-9)^2+(10-10)^2}\\\\TO=9 \text{Unit}\\\\OA=\sqrt{(18-14)^2+(10-5)^2}\\\\OA=\sqrt{4^2+5^2}\\\\OA=\sqrt{41}[/tex]
As, the Length of Adjacent sides are not equal,so it can't be a Rhombus.
The Given Quadrilateral ,"TOAD" is a Parallelogram.
⇒The Point of Intersection of both Diagonal can be Obtained by
[tex]=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})\\\\\text{Point P}=(\frac{14+9}{2},\frac{5+10}{2})\\\\\text{Point P}=(\frac{23}{2},\frac{15}{2})\\\\\text{Point P}=(\frac{18+5}{2},\frac{10+5}{2})\\\\\text{Point P}=(\frac{23}{2},\frac{15}{2})[/tex]
Intersection of both diagonals is same, diagonals bisect each other.
Point of Intersection of Diagonal is Point P
[tex]=(\frac{23}{2},\frac{15}{2})[/tex]
Part C
Distance formula
[tex]=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2)}\\\\TP=\sqrt{(\frac{23}{2}-9)^2+(\frac{15}{2}-10)^2}\\\\TP=\sqrt{\frac{25}{4}+\frac{25}{4}}\\\\TP=\frac{5}{\sqrt{2}}\\\\PA=\sqrt{(\frac{23}{2}-14)^2+(\frac{15}{2}-5)^2}\\\\PA=\sqrt{\frac{25}{4}+\frac{25}{4}}\\\\TP=\frac{5}{\sqrt{2}}\\\\PD=\sqrt{(\frac{23}{2}-5)^2+(\frac{15}{2}-5)^2}\\\\PD=\sqrt{\frac{169}{4}+\frac{25}{4}}\\\\PD=\frac{\sqrt{169+25}}{2}\\\\PD=\frac{\sqrt{194}}{2}\\\\PO=\sqrt{(\frac{23}{2}-18)^2+(\frac{15}{2}-10)^2}\\\\PO=\sqrt{\frac{169}{4}+\frac{25}{4}}\\\\PO=\frac{\sqrt{169+25}}{2}\\\\PO=\frac{\sqrt{194}}{2}[/tex]
→DP=PO
→PT=PA
Length of Segments from point of intersection of two diagonal is same.So, Diagonal are bisector of each other.
In the figure, and . Complete the following statements to prove that and are supplementary angles. and , as they are corresponding angles for parallel lines cut by a transversal. Therefore, if , then by the . Therefore, and are supplementary angles by the . ° (1) , so (2) Applying the to (1) and (2), we get . Therefore, and are supplementary angles.
The Complete sentence is shown below.
What is Congruent Supplement theorem?Two angles are congruent if they are supplements of the same angle (also known as congruent angles).
The Complete sentences will be
∠EIA ≅ ∠IKC and ∠GJB is ≅ ∠ JLD (Corresponding angles)
∠EIA ≅ ∠GJB then ∠IKC ≅ ∠ JLD (Substitution Property of Congruency)
∠IKL + ∠IKC 180° (Linear Pair Theorem)
and ∠DLH + ∠JLD =180° (Linear Pair Theorem)
Then, m∠IKL + m∠IKC = 180°
Also, ∠IKC ≅ ∠JLD
m∠IKC = m∠JLD (Subtraction Property OF Congruency)
Thus, m∠IKL + m∠JLD = 180°
As, ∠IKL and ∠JLD are supplementary angles.
But ∠DLH and ∠JLD are supplementary angles.
∠IKL ≅ ∠DLH (Congruent Supplements Theorem)
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Find the radius of a cylinder with a volume of 208 cm3 and a height of 4 cm.
Suppose ABCD is a rectangle. Find AB and AD if point M is the midpoint of
BC,AM ⊥ MD , and the perimeter of ABCD is 34 in..
Someone answered this question but Ad is not 4 and AB is not 9. . Thank you
I substitute 1 in 2
AD²=2*[(17-AD)²+(AD/2)²]----> AD²=2*[289-34AD+AD²+0.25AD²]
AD²=578-68AD+2.50AD²--------> 1.50AD²-68AD+578
1.50AD²-68AD+578=0
using a graph tool to solve the quadratic equation
see the attached figure
AD1=11.33 in
AD2=34 in----------is not solution because (AB+AD=17)
Solution is AD=11.33 in
AB=17-11.33--------> 17-11.33-----> AB=5.67 in
the answer is
AD=11.33 in
AB=5.67 in
Which expression is equivalent to (x^1/2y^16)^1/2
a coin dealer buys
a coin for $850 and sells it for $1190. Find the percent of change.
Why is 1/2 not useful as a benchmark to compare 5/8 and 9/10?
A rectangle has vertices A ( 1, 2) B (1, 7), C ( 4,7) and D (4, 2). What is the area of the rectangle
What is the solution to the equation fraction 3 over 5 n minus fraction 4 over 5 equals fraction 1 over 5 n?
Answer:
n = 2
Step-by-step explanation:
As per statement of the question we will form the equation first.
[tex](\frac{3}{5})n-\frac{4}{5}=(\frac{1}{5})n[/tex]
Now we will solve the given equation to get the solution of n.
[tex](\frac{3}{5})n=\frac{4}{5}+(\frac{1}{5})n[/tex]
[tex](\frac{3}{5})n-(\frac{1}{5})n=\frac{4}{5}[/tex]
[tex](\frac{3-1}{5})n=\frac{4}{5}[/tex]
[tex](\frac{2}{5})n= \frac{4}{5}[/tex]
Now we cross multiply the fractions
(2×5)×n = 4×5
10.n = 20
[tex]n=\frac{10}{5}=2[/tex]
Therefore answer is n = 2
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Given: ABCD rhombus, AC:BD = 4:3
Perimeter ABCD = 20 cm
Find: Area of ABCD
What is the value of m in the equation 1/2m-3/4m=16, when n = 8
What is the sum of each pair of binary integers?
a. 10101111 + 11011011
b. 10010111 + 11111111
c. 01110101 + 10101100?
Final answer:
The sums for the given pairs of binary integers are: a. 10101111 + 11011011 equals 110001010, b. 10010111 + 11111111 equals 110010110, c. 01110101 + 10101100 equals 100100001.
Explanation:
The sum of each pair of binary integers is calculated using binary addition rules, which are similar to decimal addition, but instead, you only have two digits, 0 and 1, and carry over whenever you add two 1's. Let's perform the calculations for each given pair:
a. 10101111 + 11011011 = 110001010
b. 10010111 + 11111111 = 110010110
c. 01110101 + 10101100 = 100100001
Remember to start adding from the rightmost digit (least significant bit) and move left, carrying over as necessary when the sum of two bits is 2 (binary 10).
Last year Milwaukee had the total of snow amounting to 92 inches . The normal fall is 52 1/4 inches . How much above normal was the snowfall last year .
The snowfall in Milwaukee last year was 39.75 inches above the normal amount, calculated by subtracting the normal annual snowfall from last year's total.
Explanation:The student's question is related to subtraction of two amounts to find the difference between the actual snowfall and the normal snowfall in Milwaukee.
To determine how much above normal last year's snowfall was, we subtract the normal snowfall amount from last year's total snowfall.
Last year's snowfall in Milwaukee = 92 inches
Normal annual snowfall = 52 1/4 inches
To find how much above normal the snowfall was, we calculate:
92 inches - 52 1/4 inches = 92 inches - 52.25 inches
This equals 39.75 inches above normal snowfall.
In the sandwiches mode, select the "cheese" option and observe the equation given for the preparation of a cheese sandwich. in the equation, set the number of bread slices to "2" and the number of cheese slices to "1." you will see that the product formed by these three ingredients is one cheese sandwich. suppose you have 38 bread slices and 28 cheese slices. how many cheese sandwiches can you make?
Final answer:
You can make 19 cheese sandwiches with 38 bread slices and 28 cheese slices.
Explanation:
In this scenario, you have 38 bread slices and 28 cheese slices. The equation for a cheese sandwich is 1 sandwich = 2 slices of bread + 1 slice of cheese. So, if you set the number of bread slices to '2' and the number of cheese slices to '1', you can calculate how many cheese sandwiches you can make.
First, divide the number of bread slices (38) by 2 to get the number of sandwiches that can be made with the bread: 38 / 2 = 19 sandwiches.
Next, divide the number of cheese slices (28) by 1 to get the number of sandwiches that can be made with the cheese: 28 / 1 = 28 sandwiches.
Since you can only make 19 sandwiches with the available bread, the limiting factor is the bread. Therefore, you can make 19 cheese sandwiches with the given amounts of bread and cheese.
There are c players on the Cougars hockey team. The team scored a total of 36 goals this season. One of the players, Matthew, scored 2 more goals than the average per player.
the standard addition algorithm below is being used to add three two-digit numbers 4z + 27 + x 5 equals y 14. If x, y, and z each represent a different digit from 0 to 9 what is the value of (x)(y)(z)?
Write each of the following expressions as a powers of 2: (4·25)÷(23· 1/16 )
The value obtained as the power of 2 after solving the expression, (4×2⁵) ÷ (2³ × 1/16 ) will be 2⁸.
What is an integer exponent?In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
The given expression is,
(4×2⁵) ÷ (2³ × 1/16 )
Keep the base constant and add the exponents when multiplying similar bases. Maintaining the same base while multiplying the exponents will raise a base with power to another power. When dividing two bases with similar exponents, keep the exponents of the numerator and denominator constant.
= (2² × 2⁵) ÷ (2³ × 2⁻⁴ )
= (2⁷) ÷ (2⁻¹)
= 2⁸
Thus, the values obtained as the power of 2 after solving the expression, (4×2⁵) ÷ (2³ × 1/16 ) will be 2⁸.
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In your lab, a substances temperature has been observed to follow the function T(x)=(x-2)^3+8. The turning point of the graph is where the substance changes from a solid to a liquid. Using complete sentences in your written answer, explain to your fellow scientists how to find the turning point of this function.