Kristina received $125 for her birthday. Her parents offered to pay her 3.5% simple interest per year if she would save it for at least one year. How much interest could Kristina earn?
Answer:
4.375 a year
Step-by-step explanation:
The formula is
Interest earned= principal ×interest rate×time
I=125×0.035×1=4.375
Kristina could earn $4.375 in simple interest.
Explanation:To calculate the interest Kristina could earn, we can use the formula:
Interest = Principal × Rate × Time
where Principal is the initial amount, Rate is the interest rate, and Time is the duration in years.
Plugging in the values, we have:
Principal = $125Rate = 3.5% = 0.035 (expressed as a decimal)Time = 1 yearUsing the formula, we can calculate the interest:
Interest = $125 × 0.035 × 1 = $4.375
Therefore, Kristina could earn $4.375 in simple interest.
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Plzz
Answer quick plzzzz
pls help me. question in picture
Answer:
a.) [tex](m+6)(m+10)[/tex]
Step-by-step explanation:
Factor [tex]m^2+16m+60[/tex]
Find what two numbers add up to 16, and equal 60 when multiplied:
[tex]6[/tex] and [tex]10[/tex]
[tex]6+10=16\\6*10=60[/tex]
Factor:
[tex](m+6)(m+10)[/tex]
Finito.
Answer:
(m+6)(m+10).
Step-by-step explanation:
To find this answer, we will need to determine factors of 60 that when added, they are equivalent to 16.
We can begin by listing some factors:
30 and 2
4 and 15
12 and 5
6 and 10
...
Then, we can determine which of these factors can be added together to become 16. From this, we can determine that only factors "6 and 10" become 16 when added together.
When we do this, we can see that only answer 1, (m+6)(m+10), is equivalent to the equation given.
(3x3 - 2x2 - 7x + 6) = (x + 1) synthetic division
Answer:3/2
3x3-2x2-7x+6=x+1(Multiply the numbers)
9-4-7x+6=x-1(Calculate)
11-7x=x-1(Move the terms)
-7x-x=-1-11(Collect like terms&calculate)
-8x=-12(Divide both sides by -8)
x=3/2
Synthetic division is a process used to divide a polynomial by a linear expression. Using a step-by-step process, the polynomial 3x^3 - 2x^2 - 7x + 6 is divided by x + 1. The result is a new polynomial, which represents the quotient and a remainder.
Explanation:Synthetic division is used to divide a polynomial by a linear expression. In this case, we have the polynomial (3x^3 - 2x^2 - 7x + 6) and we want to divide it by (x + 1). Synthetic division follows a specific set of steps:
Write the coefficients of the polynomial in a row: 3, -2, -7, 6. Write the root of the divisor, which is the solution to x + 1 = 0. This root is -1. Drop down the leading coefficient, which is 3 in this case. Multiply the root by the number just brought down, and write the result under the next coefficient. So, (-1)*3 = -3. Add the numbers in that column to get the next number to bring down. (-2) + (-3) = -5. Repeat steps 4 and 5 until all coefficients have been processed.
The numbers at the bottom are the coefficients of the quotient polynomial, and the remainder if any.
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a local small business will donate money to the students council based on the number of carnival tickets sold. the points shown on the graph repersent the model
Answer:
A = 5
B= 20
C= 15
D=20
Step-by-step explanation:
Answer:
A = 5
B= 20
C= 15
D=20
Step-by-step explanation:
Leia cuts congruent triangular patches with an area of 15 square centimeters from a rectangular piece of fabric that is 10 centimeters long and 6 centimeters wide. How many of the patches can Leia cut from 33 pieces of the fabric?
Answer:
132 patches
Step-by-step explanation:
First we need to find the area of the rectangular piece, multiplying the length and the width:
Area of fabric: 10 * 6 = 60 cm2
If each triangular patch has 15 cm2 of area, a fabric of 60cm2 can make 60 / 15 = 4 triangular patches.
Then, if Leia uses 33 pieces of fabric, she can make a total of 33 * 4 = 132 patches.
Answer:
132
Step-by-step explanation:
Total area'A' of rectangular piece of fabric is given by
A= length 'l' x width'w'
A= 10 x 6=> 60cm²
As there are 33 such pieces, 33 x 60=1980cm²
In order to evaluate the umber of triangles that can be made, divide total area by the area of one triangular piece
n= 1980/15
n=132
Therefore, 132 triangles can be made
Riley and Jace work at a dry cleaners ironing shirts. Riley can iron 25 shirts per hour, and Jace can iron 30 shirts per hour. Riley worked 3 more hours than Jace and they ironed 460 shirts between them. Write a system of equations that could be used to determine the number of hours Riley worked and the number of hours Jace worked. Define the variables that you use to write the system.
Answer:
25r +30j = 460r - j = 3Step-by-step explanation:
Let r and j represent Riley's hours and Jace's hours, respectively. The equations could be ...
25r +30j = 460
r - j = 3
__
The solution is (r, j) = (10, 7).
The system of equations that could be used to determine the number of hours Riley and Jace worked is: R = J + 3 and 25R + 30J = 460, where R represents the number of hours Riley worked, and J is the number of hours Jace worked.
Explanation:Let's define our variables first. Let's let J represent the number of hours Jace worked and R represent the number of hours Riley worked.
From the information given, we know that Riley worked 3 more hours than Jace. So we can write this as an equation: R = J + 3.
We also know that between them, they ironed 460 shirts. We can express this as another equation by multiplying their per-hour output by the number of hours they worked, then adding the two together: 25R + 30J = 460.
So our system of equations is: R = J + 3 and 25R + 30J = 460.
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Explain how to find the constant of proportionality for the ratio of robins to cardinals. A 2-column table with 4 rows. Column1 is labeled Cardinals with entries 5, 6, 9, 10. Column 2 is labeled Robins with entries 15, 18, 27, 30.
Answer:
Divide the number of robins by the number of cardinals for each pair of values. The ratios are the same and are a constant of proportionality of 3.
Answer :
Divide the number of robins by the number of cardinals for each pair of values. The ratios are the same and are a constant of proportionality of 3.
KEEP IN MIND THIS IS A SAMPLE RESPONSE!
What is the solution to this system? Enter the solution as an ordered pair,
(x, y).
Answer:
(-2, 5)
Step-by-step explanation:
The solution of a system is where the lines cross, or a common point they share. The lines meet at (-2, 5), so that is the solution to the system.
A greengrocers sells mangoes for 77p each.
a)
Find the greatest number of mangoes you can buy for £5.
b) How much change should you receive?
Answer:
6 mangoes
0.38 or 38p
Step-by-step explanation:
Apparently the value of the mango is £ 0.77, which means that to get the number of mangoes you can buy, you must divide this value to the amount of money you have, that is, £ 5
5 / 0.77 = 6.49
which means that it is enough for 6 mangoes.
To know the change, multiply the value of one by 6 and subtract it with £ 5, it would be the change.
6 * 0.77 = 4.62
5 - 4.62 = 0.38
That is, the change is £ 0.38 or 38p
Answer:
(a) 6 mangoes
(b) £0.38
Step-by-step explanation:
(a) The greengocers sell the mangoes for 77 p.
The greatest number of mangoes you can buy for £5 can be gotten by dividing £5 by the price of each mango (77 p). We will only pick the whole number part because number of mangoes can only be whole number.
First, we convert £5 to pence:
£1 = 100 pence
=> £5 = 5 * 100 = 500 pence
Hence, the greatest number of mangoes that can be bought is:
500 / 77 = 6.49
Since we are only picking the whole number part, the answer is 6 mangoes.
(b) The price of 6 mangoes is:
6 * 77 = 462 pence
Hence, if you take £5 (500 pence) to the store, your change should be:
500 - 462 = 38 pence
38 pence is the same as £0.38
In a probability experiment, Karen flipped a coin 92 times. The coin landed on heads 41 times. What percentage of the coin flips resulted in tails? Round to the nearest percent.
Step-by-step explanation:
Step 1: Find the probability of landing on tails
92 - 41 = tails
51 = tails
[tex]\frac{51}{92}[/tex] = probability
0.554... * 100 = probability
55% = probability
Answer: The probability of landing on a tails is 55%
Answer:
55%
Step-by-step explanation:
P(heads) = 41/92
P(tails) = 1 - P(heads)
1 - 41/92
51/92 × 100
55.43478261%
Two rigid transformations are used to map triangle JKL to triangle MNQ. The first is a translation of vertex L to vertex Q. What is the second transformation?
A reflection across the line containing LK
A reflection across the line containing JK
A rotation about point L
A rotation about point K
Answer:
Option C
Step-by-step explanation:
a rotation about point L
Answer:
CStep-by-step explanation:
a rotation about point Lgood luck man get a 100% on
Fill in the blank: 3 feet = __________ inches
Answer:
3 feet
Step-by-step explanation:
There are 36 inches in 3 feet. (there are 12 inches in a foot)
Answer:
3 ft = 36 inches
Step-by-step explanation:
We know that 1 foot = 12 inches
Multiply each side by 3
3 * 1ft = 3 *12 inches
3 ft = 36 inches
Seventy of Myra’s classmates are traveling by bus to a football game in another town. They hired 2 buses, but there were only 64 seats. The remaining 6 students had to travel in a separate van. The equation 2b + 6 = 70 represents the given scenario. What does b represent? the number of buses the number of vans the number of students who rode on each bus the total number of students going to the football game
Answer:
C. the number of students who rode on each bus.
Step-by-step explanation:
Answer:
C.the number of students who rode on each bus
Here is the equation of a circle in standard form.
(x + 10)2 + (y + 9)2 = 100
What are the coordinates of the center?
A. (-10, -9)
B. (9, 10)
C. (-9, -10)
Answer:
A
Step-by-step explanation:
The equation is in the standard form of a circle:
(x – h)^2 + (y – k)^2 = r^2
where (h,k) is the center, and r is the radius.
If we compare the 2 equations:
(x – h)^2 + (y – k)^2 = r^2
(x + 10)^2 + (y + 9)^2 = 100
We can see that the center is (-10, -9).
This is because (x- -10) will become (x+10), and (y- -9) will become (x+9).
So, choice A is correct
Answer:
A
Step-by-step explanation:
The equation of a circle in standard form is: [tex](x-h)^2+(y-k)^2=r^2[/tex], where (h, k) is the center and r is the radius.
Here, our equation is: [tex](x+10)^2+(y+9)^2=100[/tex] , which means that h = -10 and k = -9. Then, the center is (-10, -9).
The answer is A.
Find the probality of rolling a multiple of 4
Answer:8
Step-by-step explanation:
Answer:
the answer is 8
Step-by-step explanation:
Manual collects $45.18 for a fundraiser. Gerome collects $18.07 more than Manual. Cidny collects 2 times as much as Gerome. How much money does Cidny collect for the fundraiser
Answer:
$126.5
Step-by-step explanation:
45.18+18.07=67.25
67.25*2=126.5
Can someone help me finger out my homework please
Answer:
(1) w = 6.4
(2) w = -67
(3) q = 336
(4) z = -14
(5) x = 9
(6) y = 3
(7) x = 8
(8) x = -16
(9) x = 54
(10) x = 13.5
Step-by-step explanation:
Ik u need it quick so mb for not explaining. Good luck
Answer:
the first one is 6.4 i cant help with others srry im not smart either.
Step-by-step explanation:
The graph of r = 2cos5theta is symmetric about the __________.
a. y-axis only
b. x-axis only
c. origin only
d. no symmetry
The graph of r = 2cos5theta is symmetric about the x-axis only.
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given function:
[tex]r=\ 2\ \cos\ \left(5\theta\right)[/tex]
Here, the graph shown below of this function.
As, seen from the graph.
The graph is symmetric about x- axis only .
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A sociologists was investigating the ages of grandparents of high school students. From a random sample of 10high school students, the sociologist collected data on the current ages, in years, of the students' maternal grandparents. A. One of the sociologist's research questions was about the mean difference in age without regard to which grandparent is older. The interval constructed in part (a) does not address such a question. Based on the sample of high school students, give the value of the point estimate for the mean difference in age that could be used to address the sociologist's question.
Answer:
The answer for (a)(-5.96, 2.36) (b) -1.8, since the difference is negative, it can be said or determined that the age of the grandfather is older
Step-by-step explanation:
Solution
(a) From the information given,
n = 10, d =-1.8, sd = 5.81
The 95% confidence interval for the population mean difference age is computed as follows:
CI =d ±tα/2,n-1 (sd/√n)
= -1.8±t₀.₀₅/₂,₁₀₋₁ (5.81/√10)
=-1.8± 2.26 (1.84)
= -1.8 ± 4.16
= (-5.96, 2.36)
Now,
There is a 95% confidence that the mean difference in age of maternal grand parents of high school students lies between - 5.96 and 2.36
(b) The age difference is calculated as the age of grand mother minus age of grand father. the point of estimate for the mean difference is as follows:
Xd = XGM - XGF
= 69.8 -71.6
=-1.8
Therefore, since the difference is negative, it can be said or determined that the age of the grandfather is older
Note: kindly find an attached copy of the complete question and table to this example below.
The mean difference in age between grandparents is calculated by taking the absolute differences between the ages of each pair of grandparents from the sample of students and then averaging those differences.
Explanation:The sociologist's research question about the mean difference in age of grandparents without regard to which one is older requires calculating the absolute difference between the ages of each pair of maternal grandparents for the sample of high school students and then taking the average of those differences. To provide a point estimate for the mean difference in age to address the sociologist's question, let us assume we have the ages of each pair of grandparents for the 10 students. If we denote these age pairs as (G11, G21), (G12, G22), ..., (G110, G210), where G1 and G2 are the ages of the two grandparents for each student, the mean difference in age would be the sum of the absolute differences of these pairs divided by the number of pairs (10 in this case).
Mean Difference = (|G11 - G21| + |G12 - G22| + ... + |G110 - G210|) / 10
Without the actual data, we cannot provide a numerical point estimate, but this is the method that would be used to calculate it.
The picture shows a triangle.
Side Lengths: 2.1in., 4.4in., 5in.
Angle Measures: 25°, 61°, 94°
Which choice describes another triangle that can be drawn?
A. Side Lengths: 4.2in., 8.8in., 10in.
Angle Measures: 25°, 61°, 94°
B.Side Lengths: 2.1in., 4.4in., 5in.
Angle Measures: 35°, 56°, 89°
C.Neither of these choices
Answer:
A
Step-by-step explanation:
I got it correct
On some other planet, Thor stands on a bridge and throws his hammer at his brother Loki, who is at ground level. The hammer’s height h (in meters above the ground), t seconds after Thor threw it, is modeled by:
Answer:
h(0) = 3600
t=60 when it hits the ground
max height at 4050
at 15 seconds
Step-by-step explanation:
h(t) = -2t^2 + 60t +3600
When it is thrown is t=0
h(0) = -2(0) +60(0) +3600 = 3600
When it hits the ground is h(t) =0
0 = -2t^2 + 60t +3600
Factor out -2
0 = -2 (t^2 -30t -1800)
Divide by -2
0 = (t^2 -30t -1800)
Factor. What 2 numbers multiply to -1800 and add to -30
0 = (t+30) (t-60)
Using the zero product property
t+30 = 0 t-60 =0
t = -30 t = 60
Since we do not have negative time
t=60
The maximum occurs halfway between the zeros
(-30+60)/2 = 30/2 = 15
Put this into the function to find the maximum value
h(15) = -2(15)^2 + 60(15) +3600
= -2 (225) +900+3600
=4050
Answer:
Thrown at: 3600
Ground after: 60
Max height: 4050
After: 15
Step-by-step explanation:
h(t) = -2t² + 60t + 3600
h(0) = 3600
-2t² + 60t + 3600 = 0
t² - 30t - 1800 = 0
t² - 60t + 30t - 1800 = 0
t(t - 60) + 30(t - 60) = 0
(t - 60)(t + 30) = 0
t = 60, -30(not possible)
h(t) = -2t² + 60t + 3600
-2(t² - 30t) + 3600
-2(t² - 2(t)(15) + 15² - 15²) + 3600
-2[(t - 15)² - 225] + 3600
-2(t - 15)² + 450 + 3600
-2(t - 15)² + 4050
30 points!!!
AOC and BOD are diameters of a circle, centre O. prove that triangle ABD and triangle DCA are congruent by RHS.
Triangle ABD and triangle DCA can be proven congruent using the RHS congruence criterion.
Explanation:To prove that triangle ABD and triangle DCA are congruent using the RHS (Right Angle, Hypotenuse, Side) congruence criterion, we need to show that they have a right angle, an equal hypotenuse, and an equal side adjacent to the right angle.
Since AOC and BOD are diameters of the circle, we know that they are perpendicular to their respective radii.Therefore, angle AOB is a right angle, and triangle AOB is a right triangle.Since AO and BO are radii of the same circle, they have the same length, making the hypotenuse AB of triangle ABD equal to the hypotenuse BD of triangle DCA.Furthermore, angle ABD and angle CDA are both subtended by the same arc AD, so they are equal in measure.Finally, the adjacent sides to the right angles, AB and DC, are also equal as they are radii of the circle.Therefore, by the RHS criterion, triangle ABD and triangle DCA are congruent.
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Analyze the graph of the given polar curve. If possible, describe the shape of the graph (circle, rose curve, limacon, etc), and
state the domain, range, and maximum r-value of the graph. State whether the graph is continuous and whether it is
bounded. Describe any symmetry the graph has. Give the equations of any asymptotes or state that the graph has no
asymptotes.
r= 3 -3cos theta
Answer:
Step-by-step explanation:
The shape of the curve is a rose curve.
The domain are real numbers
And the range is approximately from -3.9 to 3.9
The maximum value of r on the graph is 3.9
Yes the graph is continuous and it is bounded above and below
The graph is symmetrical about the x axis and not about the y axis.
No asymptotes
He fills the pencil holder with sand before he wraps it to make it feel like a heavy, expensive gift. How much sand will he need to "borrow" from his sister's sandbox to fill the pencil holder? *
1 point
a) 21 cubic inches
b) 7.5 cubic inches
c) 9.375 cubic inches
d) 10.5 cubic inches
e) 15 cubic inches
Answer:
Answer choice d
Step-by-step explanation:
To find the volume of this triangular prism, you first need to find the area of the triangular base. The formula for the area of a triangle is bh/2, which in this case is 3*2/2=3 square units. Multiplying this by the height of the prism, 3.5, you get a total of 10.5 cubic inches, or answer choice d. Hope this helps!
An A-frame house is 45 feet high and 32 feet wide. Find the measure of the angle that the roof makes with the floor. Round to the nearest degree.
Answer:
Angle, [tex]\theta=70.4^{\circ}[/tex]
Step-by-step explanation:
We have, an A-frame house is 45 feet high and 32 feet wide. It is required to find the measure of the angle that the roof makes with the floor.
The attached figure shows the A frame. Let [tex]\theta[/tex] is the angle that the roof makes with the floor. So,
[tex]\tan\theta=\dfrac{45}{16}\\\\\tan\theta=2.81\\\\\theta=\tan^{-1}(2.81)\\\\\theta=70.4^{\circ}[/tex]
So, the angle of 70.4 degrees is the angle that the roof makes with the floor.
Final answer:
To find the angle an A-frame house roof makes with the floor, one needs to use trigonometry. By dividing the width of the house by 2 to work with a right triangle and using the tangent function, the angle is calculated to be approximately 70 degrees.
Explanation:
The question involves finding the angle that an A-frame house roof makes with the floor, given the height of the house is 45 feet and the width is 32 feet. To solve this, we can use trigonometry, specifically the tangent function, as we are dealing with a right-angled triangle where the house's height forms one leg (opposite) and half of the width forms the other leg (adjacent). The formula to find the angle (θ) is θ = arctan(opposite/adjacent).
First, halve the width to work with one side of the A-frame: 32 feet / 2 = 16 feet. Then, use the arctan function: θ = arctan(45 feet / 16 feet). Use a calculator to find θ, which gives us an angle of approximately 70.346 degrees. When rounded to the nearest degree, the angle is 70 degrees.
Therefore, the angle that the roof makes with the floor is 70 degrees.
Choose ONE of the equations to solve. SHOW DETAILED WORK & give the answer.
Answer:
x=3
Step-by-step explanation:
9x+5+2x = 38
Combine like terms
9x+2x +5 = 38
11x+5 = 38
Subtract 5 from each side
11x+5-5 = 38-5
11x = 33
Divide each side by 11
11x/11 = 33/11
x = 3
Answer:
3(2n + 10) = 54
n = 4
Step-by-step explanation:
3(2n + 10) = 54
Divide both sides by 3
2n + 10 = 18
Subtract 10 form both sides
2n = 8
Divide both sides by 2
n = 4
How many 350 mL cans of coke can be filled from a 20.3 L tank of coke?
Answer:
x = 58
Step-by-step explanation:
We know that,
1 mL = 0.001 L
So, 350 mL = 0.35 L
Let x cans of coke can be filled from a 20.3 L tank of coke. So,
Accoding to question,
[tex]0.35\times x =20.3\\\\x=\dfrac{20.3}{0.35}\\\\x=58[/tex]
So, there are 58 350 mL cans of coke that can be filled from a 20.3 L tank of coke.
13.5-ounce bottle cost 2.19. A 29.2-ounce bottle costs 5.37 find the unit price for each size
Answer:
A)Unit prize is $0.162
B)Unit prize is $0.183
Step-by-step explanation:
A) 13.5-ounce bottle cost 2.19
Cost of 13.5 ounce bottle =2.19
Cost of 1 ounce bottle =[tex]\frac{2.19}{13.5}=0.162[/tex]
So, Unit prize is $0.162
B)29.2-ounce bottle costs 5.37
Cost of 29.2 ounce bottle = 5.37
Cost of 1 ounce bottle =[tex]\frac{5.37}{29.2}=0.183[/tex]
So, Unit prize is $0.183
Find the value of csc theta, if cos =-3/5; 90 degrees < theta < 180 degrees
Answer:[tex]\frac{5}{4}[/tex]
Step-by-step explanation:
Given
[tex]\cos \theta =\frac{-3}{5}[/tex]
and [tex]\theta [/tex] lies between
[tex]90^{\circ}<\theta <180^{\circ}[/tex]
and for this [tex]\theta[/tex],[tex]\sin[/tex] and [tex]\text{cosec}[/tex] is Positive as they lie in 2 nd Quadrant
[tex]\sin ^2\theta +\cos ^2\theta =1[/tex]
[tex]\sin ^2\theta =1-(\frac{-3}{5})^2[/tex]
[tex]\sin ^2\theta =1-\frac{9}{25}[/tex]
[tex]\sin ^2\theta =\frac{16}{25}[/tex]
[tex]\sin \theta =\frac{4}{5}[/tex]
[tex]\therefore \text{cosec}\ \theta =\frac{5}{4}[/tex]