Nickel = 0.05
Dime = 0.10
XNickels + YDimes = 3.25
0.05X + 0.1Y = 3.25
You could do this using trial and error.
You know the maximum amount of dimes you could have is 32. Because 32 * 0.1 = 3.20. If you had 33 dimes, you'd go over the limit.
You also know you need to have 48 coins. If you have 32 dimes and 1 nickel, you will not have 48 coins.
You can try any number below 32. I will try 16 because it's half of 32.
16 * 0.1 = 1.60
48 - 16 = 32 coins left
32 * 0.05 = 1.60
1.60 + 1.60 = 3.20
We're a nickel off, therefore we need to remove a nickel and add a dime.
17 * 0.1 = 1.70
48 - 17 = 31
31 * 0.05 = 1.55
1.70 + 1.55 = 3.25
Jessica will have 17 Dimes and 31 Nickels.Jessica has about 31 nickels, 17 dimes which is worth $3.25
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the number of nickels and y represent the number of dimes.
x + y = 48 (1)
Also:
0.05x + 0.1y = 3.25 (2)
x = 31, y = 17
Jessica has about 31 nickels, 17 dimes which is worth $3.25
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Find the circumference of a circle with radius,
r
= 7.5m.
Give your answer rounded to 1 DP.
Answer: C≈47.12m
Step-by-step explanation:
C=2π r=2· π· 7.5≈47.12389m
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x^2=4^2+4^2 Pythagorean theorem
Answer: 5.6?
Step-by-step explanation:
x^= 16+16
x^= 32
find the square root of 32 which is 5.6 pretty sure
Justin receives $15 and puts it into his savings account. He adds $0.25 to the account each day for a number of days, d, after that. He writes the expression 15+0.25(d−1) to find the amount of money in his account after d days. Which statement about his expression is true?
a. It is the sum of the initial amount and the additional amount after d days.
b.It is the product of the initial amount and the additional amount after d days.
c.It is the sum of the initial amount and the number of days, d.
d.It is the difference between the initial amount and the additional amount after d days.
Answer:
expression a
Step-by-step explanation:
The given expression is 15+0.25(d−1).
let suppose,
15 = a
0.25(d−1) = b
we get a + b
It clearly indicates the given expression is sum of two entities, we can exclude option b and option d.
Now we are left with option a and c, for that we have to evaluate the term b
b = 0.25(d−1) that is the additional amount after d days
Therefore, expression a is correct.
Answer:
It is the sum of the initial amount and the additional amount after d days.
Step-by-step explanation:
It is the sum of the initial amount and the additional amount after d days. i have ttm
Pls help me with number and thanks!
Answer:
the answer would be 3,-5
Step-by-step explanation:
you rotate it in a 90 degree clockwise rotation and you end up with 3,5 and when you reflect it upon the x-axis your point ends up at 3,-5
Answer:
3,-5
Step-by-step explanation:
If you rotate it in a 90 degree rotation in the clock direction you will end in 3.5 and your x-axis will result in 3.5.
Find the distance between the two points. Round to the nearest tenth if necessary. (6, 11), (0, 3) a. 10 b. 14 c. 15 d. 100
Answer: option a
Step-by-step explanation:
You must apply the formula for calculate the distance between the two points. which is shown below:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Therefore, keeping on mind that the points given in the problem are (6, 11), (0, 3), when you substitute values into the formula shown above, you obtain that the distance between these two points is the following:
[tex]d=\sqrt{(0-6)^2+(3-11)^2}\\d=10[/tex]
Answer:
a. 10
Step-by-step explanation:
We have been given two points (6, 11) and (0, 3). Now we need to find the distance between points (6, 11) and (0, 3) and check which of the following choices are correct:
(6, 11), (0, 3) a. 10 b. 14 c. 15 d. 100
Also we should round to the nearest tenth if necessary.
Apply distance formula :
[tex]distance =\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
[tex]distance =\sqrt{\left(0-6\right)^2+\left(3-11\right)^2}[/tex]
[tex]distance =\sqrt{\left(-6\right)^2+\left(-8\right)^2}[/tex]
[tex]distance =\sqrt{36+64}[/tex]
[tex]distance =\sqrt{100}[/tex]
[tex]distance =10[/tex]
Hence correct choice is a. 10
You plan to buy a DVD player 10 weeks from now. If the DVD player costs $260, how much money must you save each week in order to buy it? "Work must be shown."
$260 divided by 10 weeks equals $26 a week
In each case, determine if the sides form a right triangle. If they do, place in the Yes column. If not, place them in the No column.
The question is asking to determine whether given sets of sides form a right triangle using Pythagorean theorem. The theorem is verified if the square of the length of the longest side equals the sum of the squares of the two other sides. However, some approximations might not perfectly fit the theorem but still form a right triangle.
Explanation:The subject of this question is the Pythagorean Theorem in the field of Mathematics. The theorem is a fundamental principle in Geometry which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² = b² + c².
To determine whether or not a set of sides forms a right triangle, you would need to check if the lengths satisfy the Pythagorean theorem. If they do, then the sides are potentially those of a right triangle. For instance, if you're given sides with lengths 3, 4, and 5, you can check if 5² equals 3² + 4². Since 5² = 25 and 3² + 4² = 9 + 16 = 25, the sides do form a right triangle.
However, checking with the Pythagorean theorem is only conclusive if the lengths already satisfy the theorem. There might be situations where the length measurements are approximations and might not perfectly fit the theorem despite forming a right triangle.
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what is the following difference 11 sqrt 45 - 4 sqrt 5
Answer:
29*sqrt(5)
Step-by-step explanation:
Start with sqrt (45). You must reduce it to it's prime factors.
45: 9 * 5 9 is not prime so reduce it.
45: 3 * 3 * 5
When you write √45, you should replace it with √(3*3*5)
The rule is
Rule: when you have a pair of equal prime factors under a root sign, you can take one out and throw one away.
Rule 2: If there are an odd number of equal primes one of them will be left underneath the root sign.
√45 = 3√5
11sqrt(45) - 4 sqrt(5) Substitute for 45
11*3*sqrt(5) - 4sqrt(5) Take out sqrt(5) using the distributive property.
(11*3 - 4)*sqrt(5) Combine 11 * 3
(33- 4) * sqrt(5) Do the subtraction
29 * sqrt(5) Answer
The correct answer is 29[tex]\sqrt{5}[/tex]
The third option.
Has anyone taken the PERT test? If so, what was the math like? Please give me a rundown of the math if you have taken it. I’m really worried about this part of the test. Thank you!
Answer:
Step-by-step explanation:
yes i did and it was sad because it was so hard mabey some questions where easy but other than that it was hard i whould cry throught the whole pert test but nah i didint
The PERT test's Math portion mainly covers algebra and geometry. It includes topics such as fractions, decimals, percentages, ratios and proportions, linear equations, inequalities, polynomials, quadratic equations, and basic geometry concepts. Preparation, practice, and study guides are recommended to perform well.
Explanation:The PERT (Postsecondary Education Readiness Test) is a placement test used by colleges in Florida to assess a students' college readiness in Reading, Writing, and Mathematics. If you're concerned about the Math section, understanding the content breakdown can be very helpful.
The Math portion of the PERT test primarily includes algebraic and geometry questions, with the main focus being algebra. Topics include but aren't limited to fractions, decimals, percentages, ratios and proportions, linear equations, inequalities, polynomials, quadratic equations, and basic geometry concepts.
Preparing for this test may include using study guides, practice tests, and brushing up on your algebra and geometry skills. Remember utilizing all available resources and allotting ample time to study can greatly help you perform better on the test.
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What is the answer to this please?
Answer:
D
Step-by-step explanation:
The sides of a regular hexagon are congruent
Given that 1 side = 15in, then
perimeter = 6 × 15 = 90 in → D
Find the cost of one item to the nearest cent. Round if necessary. 8 lbs. of apples for $9.52
Answer:
76.16
Step-by-step explanation:8 multiplied by 9.52
If a parallelogram is inscribed in a circle, then it must be a? A. Triangle B.rhombus C. Rectangle D. Trapezoid
The answer for your question is:
C: Rectangle
If a parallelogram is inscribed in a circle, then it must be a Rectangle
What is a parallelogram?Any quadrilateral in which opposites sides are parallel is called a parallelogram.
What is a triangle?Any 2 dimensional figure bounded by 3 sides and sum of all the angles is 180° is called a triangle.
What is a rhombus?A parallelogram with four equal sides and sometimes one with no right angles is called a rhombus.
What is a rectangle?A rectangle is a four sided quadrilateral, having all the internal angles equal to 90 degrees and opposite sides are equal.
What is a trapezoid?A trapezoid is a quadrilateral with one pair of opposite sides parallel.
How to know what the parallelogram will be if it is inserted in a circle ?We know that if a quadrilateral is inscribed in a circle then the sum of its opposite sides will be supplementary (180°)We know that all the angles of a rectangle is 90°. So sum of opposite angles will be 180°.This follows the characteristics features of a circle.
So the required parallelogram will be a rectangle.
Option C is correct.
In rhombus and trapezoid the sum of opposite angles are not 180°.A triangle is not a parallelogram.So, options A , B, D are incorrect.
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Which set of data contains two outliers
Answer:
you need to list the sets of data.
Step-by-step explanation:
what is the expression of 3/4 times 5/7 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
3 x 5 = 15
4 x 7 = 28
the answer is 15/28
;)
HELP!
Find the difference: 45.6 - 0.01
A) 35.6
B) 44.59
C) 44.6
D) 45.59
It would be D because 45.60-.01 would mean you subtract the .01 from the .60
Answer:
D)4.193
Step-by-step explanation:
how many eighths of an inch are in 1/4
Answer:
One eighth is one part of eight equal sections. Two eighths is one quarter and four eighths is a half. It's easy to split an object, like a cake, into eighths if you make them into quarters and then divide each quarter in half.
There are two eighths of an inch in a quarter of an inch.
Explanation:The student is asking how many eighths of an inch are in 1/4 of an inch. To get the answer, you have to ask "how many 1/8's fit into 1/4". Since 1/4 is the same as 2/8, there are two eighths in one quarter.The student is asking how many eighths of an inch are in 1/4 of an inch. To get the answer, you have to ask "how many 1/8's fit into 1/4". Since 1/4 is the same as 2/8, there are two eighths in one quarter.The student is asking how many eighths of an inch are in 1/4 of an inch. To get the answer, you have to ask "how many 1/8's fit into 1/4". Since 1/4 is the same as 2/8, there are two eighths in one quarter.
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A passenger in an airplane flying at an altitude of 37,000 feet sees two towns directly to the west of the airplane. The angles of depression to the towns are 32° and 76°. How far apart are the towns?
Answer:
[tex]49,987.24\ ft[/tex]
Step-by-step explanation:
Let
x-----> distance from the two towns
we know that
In the right triangle ABC
[tex]tan(32\°)=37,000/(x+y)\\x+y=37,000/tan(32\°)[/tex]
In the right triangle ABD
[tex]tan(76\°)=37,000/(y)\\y=37,000/tan(76\°)[/tex]
see the attached figure to better understand the problem
Remember that
(x+y)-y=x
so
[tex]x=\frac{37,000}{tan(32\°)} -\frac{37,000}{tan(76\°)}[/tex]
[tex]x=49,987.24\ ft[/tex]
Find the doubling time of an investment earning 7% interest if interest is compounded continuously
Answer:
The doubling time of this investment would be 9.9 years.
Step-by-step explanation:
The appropriate equation for this compound interest is
A = Pe^(rt), where P is the principal, r is the interest rate as a decimal fraction, and t is the elapsed time in years.
If P doubles, then A = 2P
Thus, 2P = Pe^(0.07t)
Dividing both sides by P results in 2 = e^(0.07t)
Take the natural log of both sides: ln 2 = 0.07t.
Then t = elapsed time = ln 2
--------- = 0.69315/0.07 = 9.9
0.07
The doubling time of this investment would be 9.9 years.
To calculate the doubling time for an investment earning 7% interest compounded continuously, the Rule of 70 is used, which suggests that the investment will double in approximately 10 years.
To find the doubling time of an investment earning 7% interest compounded continuously, we can use the Rule of 70. The Rule of 70 is a quick and useful formula that estimates the number of years it takes for an investment to double given a fixed interest rate, specifically for interest rates below 10%. Here's how you can use it:
Take the number 70 and divide it by your interest rate. In this case, the interest rate is 7%.The formula looks like this: Doubling Time (in years) = 70 / interest rate.Therefore, the doubling time for an investment earning a 7% interest rate is approximately 70 / 7, which equals 10 years.The Rule of 70 assumes continuous compounding. Thus, if an investment has a consistent return of 7% per year, compounded continuously, it will take roughly 10 years to double.
It's also worth noting that the Rule of 72 can be used in a similar way to estimate the doubling time more roughly. In this case, using the Rule of 72, dividing 72 by the interest rate of 7% would provide an estimation of approximately 10.3 years. This is a close approximation and often used due to its simplicity.
There are 3.5 times as many cats as there are dogs. If there are 28 dogs, how many cats are there?
Answer:98 I believe
Step-by-step explanation:
Answer:
98.
Step-by-step explanation:
Number of cats = 28 * 3.5
= 98 cats.
That's a zoo!!
a computer store sells computers for 10% more than they pay for them . if the store pays x dollars for a computer , which expression would represent the prince for which the store would sell the computer? a. 0.10x / b. 0.9x / c.1.1x / d. 10x
Answer: C
Explanation:
If a store paid x dollars to buy the computer and they sold it for 10 percent extra, it would be x+.1x. We can use the distributive property to get that x+.1x=x(1+.1) to get 1.1x, or C
Answer: c.1.1x
Step-by-step explanation:
Hi, the correct option is c.1.1x.
Since the price they paid for the computer is 100%, if they sell them for 10% more:
100%+10% =110% (sales percentage)
So, for a price x, to obtain the selling price we have to multiply the price (x) by the sales percentage in decimal form (110/100= 1.1)
The final expression is:
1.1x
multiplying mixed numbers and whole numbers 1 1/2 x 2/1 =
Answer: 3
Step-by-step explanation:
1. Convert the mixed number to fraction:
- Multiply the denominator of the fraction by the whole number.
- Add the product obtained and the numerator of the fraction.
- Write the sum obtained as the numerator and rewrite the original denominator of the fraction.
Then:
[tex]1\ 1/2=\frac{(1)(2)+1}{2}=\frac{3}{2}[/tex]
2. Multiply the numerators.
3. Multiply the denominator.
4. Reduce the fraction.
Then:
[tex](\frac{3}{2})(\frac{2}{1})=\frac{6}{2}=3[/tex]
Find the area of the figure to the nearest tenth.
31.5in² hopefully this helps
The area of a sector can be calculated using a given formula. After adjusting for the given radius and angle, the approximate area of the sector is 31.1 cm^2.
Without specifications about the figure, let's consider it as a sector of a circle.
The area of a sector can be calculated using the formula Area = (angle / 360) * π * (radius)^2.
But here we are given the base length, which is actually the diameter for the whole circle.
Hence, the radius would be base/2 which is 9/2 = 4.5 cm.
So, by substituting the given values in the formula, the area will be Area = (140 / 360) * π * (4.5)^2 = 31.07 cm^2 approx. So, the area of the figure to the nearest tenth is 31.1 cm^2.
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How many square feet of outdoor carpet will we need for this hole
I say 8 is the answer.
Proof:
[tex]3 + 2 + 3 = 8[/tex]
So 8ft is my answer.
Answer:
36 square feet outdoor carpet will be required for this hole.
Step-by-step explanation:
A triangle colored in green with a rectangular hole has been given in the figure.
Area of the outdoor carpet will be calculated by the expression,
Area of the carpet = Area of the right triangle - Area of the rectangle removed from the triangle
Area of the right triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}\times (12)\times (7)[/tex]
= 42 square ft
Area of the rectangle = Length × Width
= 3×2
= 6 square ft
Area of the remaining area to be covered with the carpet = 42 - 6
= 36 square feet
Therefore, area of the outdoor carpet required for the hole = 36 feet²
write a rule for the sequence then find the next three terms 24,27,30,33 . . .
The rule is add 3. The next three terms are 36, 39, 42
How many solutions does this system have?
The system has Infinite solutions
If a 13-foot ladder makes a 58 angle with the ground, how many feet up a wall will it reach? Round your answer to the nearest tenth.
Answer:
11.02 = a, rounded to the nearest 10th
Step-by-step explanation:
The length of the ladder (13 ft) forms the hypotenuse of the triangle when leaned against the house. The distance the ladder goes up the wall is the side opposite to the angle we are working with, so we can use the sine function to solve.
Sin X = (opposite side)/(hypotenuse)
Sin 58 = a/13
13(Sin 58) = a
11.02462525 = a
11.02 = a, rounded to the nearest 10th
A 13-foot ladder making a 58-degree angle with the ground will reach approximately 6.9 feet up a wall when we use the cosine function to calculate the height.
To find how many feet up a wall a 13-foot ladder will reach when it makes a 58-degree angle with the ground, we can use trigonometric functions, specifically the cosine function for adjacent and hypotenuse in a right-angled triangle.
The formula we will use is:
cosine(angle) = [tex]\frac{height}{hypotenuse}[/tex]
Re-arranging the equation to solve for the adjacent side, we get:
adjacent side = cosine(angle) * hypotenuse
Now plug in the values:
adjacent side = [tex]cosine(58 ^0) * 13 feet[/tex]
We can calculate the cosine of 58 degrees using a calculator and multiply it by 13, which will give us the height the ladder reaches on the wall. Let's calculate:
adjacent side = 0.5299 * 13 feet
adjacent side = 6.8887 feet
Therefore, a 13-foot ladder at a 58-degree angle with the ground will reach approximately 6.9 feet up a wall.
Which is an equation of a direct proportion?
a.y=1/6x+6 b.y=6/x
c.y=6x-6 d.y=6x
Answer:
Option D. y=6x
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
Verify each case
case a) y=(1/6)x+6
Is a linear equation, but is not a direct variation. The line not passes through the origin
case b) y=6/x
The equation represent an inverse variation
case c) y=6x-6
Is a linear equation, but is not a direct variation. The line not passes through the origin
case d) y=6x
The equation represent a direct variation
Final answer:
Among the options provided, option d. y = 6x is the equation of a direct proportion because it follows the form y = kx where k is the constant of proportionality and there is no added or subtracted constant.
Explanation:
The equation of a direct proportion is one where the dependent variable changes at the same rate as the independent variable. In mathematical terms, if two variables y and x are directly proportional, it implies that y = kx, where k is the constant of proportionality.
Looking at the options provided:
a. y = 1/6x + 6 is not directly proportional because of the addition of the constant 6.
b. y = 6/x is an inverse proportion because y changes inversely with x.
c. y = 6x - 6 is also not directly proportional due to the subtraction of the constant 6.
d. y = 6x perfectly fits the definition of direct proportionality as there is no added or subtracted constant and it follows the form y = kx.
Therefore, the equation of a direct proportion among the options given is d. y = 6x.
Using similar triangles to find an unknown value. What is the value of x?
Solve the system of equations
y=x-3
y=x^2-5x+6
Answer:
x=3 (double root)
Step-by-step explanation:
We are told that y = x - 3.
Substituting x - 3 for y in the second equation yields:
x - 3 = x² - 5x + 6.
We need to rewrite this in the standard form of a quadratic equation:
Subtracting (x - 3) from both sides results in:
0 = x² - 5x + 6 - x + 3.
Combining like terms gives us:
0 = x² - 6x + 9,
which factors into (x - 3)(x - 3) = 0. Thus, there are two real, equal roots: x = 3 and x = 3.
Subbing 3 for x in the first equation gives us 3 - 3 = 0 = y..
Thus, the solution of this system of equations is (3, 0).
Answer:
(3,0)
Step-by-step explanation:
one side of a sqaure is 10 units which is greater, the number sqaure units for the area of the sqaure or the number of units for the preimeter explain
The area is greater because you multiply 10 by 10. The perimeter is all the sides added together so that would be 40 units. All sides of the square are the same. Area is length times width
The area of a square with a side of 10 units is 100 square units, which is greater than its perimeter of 40 units, because the area measurement squares the side's length, whereas the perimeter is a sum of side lengths.
To determine which is greater between the area of a square and its perimeter, we start by understanding that the area of a square is calculated by squaring the length of one side. In this case, the square's side is 10 units, so the area is 10 units imes 10 units = 100 square units. The perimeter of a square is the sum of all its sides, which is 4 times the length of one side. Hence, the perimeter is 10 units times 4 = 40 units.
As a result, the area, which is 100 square units, is greater than the perimeter, which is 40 units. This demonstrates that while the perimeter is a measure of the distance around the square, the area represents the entire space enclosed within it, leading to larger numerical values when the sides of the square are squared as opposed to simply multiplied by four.