Answer:
He is correct.
Step-by-step explanation:
9÷4=2.25
The equivalent quarterly interest rate is 2.25%. The annual interest is converted quarterly by dividing the annual rate by 4.
What is the definition of simple interest?Simple interest is a notion employed in various industries, including banking, finance, and automobiles.
Gavin put money into his savings account, which is compounded annually at an interest rate of 9%
The corresponding quarterly interest rate is, 2.25%.
The annual interest is converted quarterly as;
[tex]\rm n= \frac{9}{4} \\\\ n= 2.25\%[/tex]
Hence, the equivalent quarterly interest rate is 2.25%.
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Kelly read 40% of a novel, and she now has 108 pages left. How many pages does the novel have?
Answer:
The novel has 180 pages.
Step-by-step explanation:
108 pages is 60% of the novel.
108 / 3 = 36.
20% of the novel is 36 pages.
36 * 5 = 180 pages
A bag contains colored marbles. The ratio of red marbles to blue marbles is 1 : 4. The ratio of blue marbles to yellow marbles is 2 : 5. What is the ratio of red marbles to yellow marbles?
Final answer:
To find the ratio of red to yellow marbles, given the ratios of red to blue and blue to yellow, we equalize the blue part of both ratios and combine them, resulting in a red to yellow ratio of 2:5.
Explanation:
The question concerns finding the ratio of red marbles to yellow marbles given the ratios of red to blue marbles and blue to yellow marbles. To solve this, we use the given ratios: the ratio of red marbles to blue marbles is 1 : 4, and the ratio of blue marbles to yellow marbles is 2 : 5. Firstly, we make the number of blue marbles consistent in both ratios by finding a common value. Multiplying the first ratio by 2 gives us red to blue as 2 : 8, and keeping the second ratio as is (blue to yellow as 2 : 5), we can now combine these to find the ratio of red marbles to yellow marbles. The red to yellow ratio, through the intermediary blue, becomes 2 : 5.
Fill in the missing angle measures
Yo sup??
by angle sum property we know that the sum of all angles in a triangle is 180
let the unknown angle be x
then,
x+60+90=180
x=180-150
x=30
Hope this helps
The sum of the angles of a triangle is 180°.
The angle measures you know are 60° and 90° (because the box in the top right corner of the triangle means that it is a right angle, which equals 90°). So you can do this to find the missing angle:
60° + 90° + ? = 180° Add 60 and 90
150° + ? = 180° Subtract 150 on both sides
? = 30° The missing angle is 30°
(6x10^-6) (5.2x10^4 scientific notation
Step-by-step explanation:
[tex](6 \times {10}^{ - 6} )(5.2 \times {10}^{4} ) \\ = 6 \times 5.2 \times {10}^{ - 6} \times {10}^{4} \\ = 31.2 \times {10}^{4 - 6} \\ = 31.2 \times {10}^{ - 2} \\ = 0.312 \\ = 3.12 \times {10}^{ - 1} [/tex]
Does 27/8 equal 2 7/8
No if you simplify 27/8 it equals 3 3/8.
Question 3
Mr. Winking is purchasing a car and needs to finance $24,000 from the bank with an annual percentage rate (APR) of
4.8%. He is financing it over 5 years and making monthly payments. What is the monthly payment?
$104.54
$378.21
$450.71
$1225.56
Answer:
The monthly payment, PMT = $450.71
Therefore the correct option is C.) $450.71
Step-by-step explanation:
i) Value of Loan, or Present value, PV = 24000
ii) Annual percentage rate , APR = 0.048
iii) number of periods, n = 12
iv) periodic interest, R = APR / n = 0.048 / 12 = 0.004
v) number of years, t = 5
v) Monthly Payment, PMT = [tex]\frac{PV\times R}{1 - (1 + R)^{(-1\times n \times t})} = \frac{24000 \times 0.004}{1 - ( 1 + 0.004)^{-60}}[/tex] = $450.71
Find the equation for the circle with center (-4,-5) and passing through (4,-2)
Answer:
(x + 4)² + (y + 5)² = 73
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
here (h, k) = (- 4, - 5), thus
(x - (- 4))² + (y - (- 5))² = r², that is
(x + 4)² + (y + 5)² = r²
The radius is the distance from the centre to a point on the circle.
Calculate r using the distance formula
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 4, - 5) and (x₂, y₂ ) = (4, - 2)
r = [tex]\sqrt{(4+4)^2+(-2+5)^2}[/tex]
= [tex]\sqrt{8^2+3^2}[/tex]
= [tex]\sqrt{64+9}[/tex] = [tex]\sqrt{73}[/tex] ⇒ r² = 73, thus
(x + 4)² + (y + 5)² = 73 ← equation of circle
Answer: [tex](x+4)^{2} +(y+5)^{2} = 73[/tex]
Step-by-step explanation:
the formula for finding equation of circle is given as :
[tex](x-a)^{2}+(y-b)^{2} = r^{2}[/tex]
where ( a,b) is the coordinate of the center and r is the radius
The radius is the distance between the point and the center , the formula for calculating the distance between two points is given by :
d = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
d = [tex]\sqrt{(4-(-4))^{2}+(-2-(-5))^{2}}[/tex]
[tex]d = \sqrt{(4+4)^{2}+(-2+5)^{2}}[/tex]
[tex]d = \sqrt{8^{2}+3^{2}}[/tex]
[tex]d = \sqrt{73}[/tex]
since "r" is the distance , then
[tex]r = \sqrt{73}[/tex]
The the equation of the circle , using the formula [tex](x-a)^{2}+(y-b)^{2} = r^{2}[/tex] , will be
[tex](x+4)^{2} +(y+5)^{2} = 73[/tex]
73. Given PQRS is a parallelogram.
PR bisects Angle SPQ and Angle QRS.
SQ bisects Angle PSR and Angle RQP.
Prove PQRS is a rhombus.
Answer:
See explanation
Step-by-step explanation:
PQRS is a parallelogram, then
[tex]PQ\parallel RS\\ \\QR\parallel SP[/tex]
and
[tex]PQ\cong RS\\ \\QR\cong SP[/tex]
Also
[tex]\angle P\cong \angle R\\ \\\angle Q\cong \angle S[/tex]
1. Consider triangles PQA and RQA, where A is the diagonals intersection point. In these triangles,
[tex]QA\cong QA\ [\text{Reflexive property}][/tex]
[tex]\angle PQA\cong \angle RQA\ [\text{Because QS is angle bisector}][/tex]
[tex]\angle QPA\cong \angle QRA\ [\text{Diagonal PR divides congruent angles in congruent halves}][/tex]
Hence, by AAS postulate triangles PQA and RQA are congruent. Congruent triangles have congruent corresponding parts, so
[tex]PQ\cong RQ[/tex]
2. Consider triangles PSA and RSA. In these triangles
[tex]SA\cong SA\ [\text{Reflexive property}][/tex]
[tex]\angle PSA\cong \angle RSA\ [\text{Because QS is angle bisector}][/tex]
[tex]\angle SPA\cong \angle SRA\ [\text{Diagonal PR divides congruent angles in congruent halves}][/tex]
Hence, by AAS postulate triangles PSA and RSA are congruent. Congruent triangles have congruent corresponding parts, so
[tex]PS\cong RS[/tex]
3. Since [tex]PQ\cong RS[/tex] and [tex]PQ\cong RQ[/tex], you have [tex]RS\cong RQ[/tex]
Therefore,
[tex]PQ\cong QR\cong RS\cong SP[/tex]
Parallelogram with all congruent sides ia a rhombus.
Miss Jacobs purchase 10.2 ounces of candy for her class. Each student gets 0.85 ounces. Right and solve an equation to determine how many students are in Miss Jacobs class.
Answer:
There are 12 students in Miss Jacobs class.
Step-by-step explanation:
Divided 10.2 and 0.85
If you check your answer. 0.85 multiplied by 12 is 10.2
How many square inches of wrapping paper will he need?
The area of circular garden is 615.44 feet2. What is the circumference of the garden? (Use 3.14 for .)
A.
205.15 feet
B.
87.92 feet
C.
43.96 feet
D.
307.72 feet
Answer:
B.)
87.92 feet
Step-by-step explanation:
Given:
Area of the circular garden [tex]= 615.44 ft^2[/tex]
[tex]\pi =3.14[/tex]
Finding the radius of the circle.
Area of the circle= [tex]\pi r^2[/tex]
[tex]615.44=\pi *r^2[/tex]
[tex]r^2=\frac{615.44}{\pi } \\\\r^2=\frac{615.44}{3.14} \\r^2=196\\r=14 ft.[/tex]
Circumference of the garden:
[tex]=2\pi r\\=2*3.14*14\\=87.92ft.[/tex]
Elsa can type 75 words per minute on a Keyboard
Elsa's rate of typing = 1.25 words per sec
Time is taken for typing each word = 0.8 a
What is unitary method used?It is a method of solving by finding the value of one unit and the calculating the value of given unit by multiplying with the single value.
Step by step calculationNumbers of words Elsa can type in 1 minute(the 60s) = 75
Numbers of words Elsa can type in one second = 75/60
∴ Rate of typing = 1.25 words per sec
Time is taken to type one word = 60/75
= 0.8 sec
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Henry’s disability insurance pays 70% of his salary for up to 26 weeks if his salary is $450 and he is disabled for 20 weeks how much disability will he get?
Answer:
$1575
Step-by-step explanation:
70 % of his salary is 0.7 X 450 = 315
He gets it for 20 weeks
presuming the salary is monthly.
You do 315 X 5 = 1575 20 /4 = 5 months
The length of the base of an isosceles triangle is x. The length of a leg is 3x -4. The perimeter of the triangle is 41. Find x.
Length of base of isosceles triangle, x = 7
Step-by-step explanation:
Step 1: Given base of isosceles triangle, x = 7 and perimeter = 41Length of one leg = 3x - 4. Since two sides, other than the base of an isosceles triangle are equal, the length of the other leg = 3x - 4.
Step 2: Formula for perimeter of triangle = length of sidesStep 3: Substitute values of sides in the formula⇒ 41 = x + (3x - 4) + (3x - 4) = x + 2(3x - 4)
⇒ 41 = x + 6x - 8
⇒ 41 = 7x - 8
⇒ 49 = 7x
⇒ x = 7
Answer:
7
Step-by-step explanation:
find the rule solve for n please help me
Answer:
Your answer is 9
Step-by-step explanation:
the answer is nine because if you look at the pattern, every number to the left is times 3 to the right. For example, 4 to 12 is times 3. this would work for n because 9x3 equals 27. the rule is times three.
I need help with please ASAP but A is not the answer
Answer:
d
Step-by-step explanation:
[tex]-\frac{6}{5}[/tex] is rational
3.5 is rational
0.5 repeating is rational
[tex]\sqrt{4}[/tex] is rational
[tex]\sqrt{5}[/tex] is NOT rational
The answer correct answer is D.
Recall that the perimeter of a rectangle is P=2(W+L), where W is the width and L is the length.
The length of a rectangle is 26 feet more than the width. If the perimeter is 60 feet, then what is the length of the rectangle,
To find the length of the rectangle, use the given information about the width and perimeter. Solve the equations to find the values of the variables and determine the length of the rectangle.
Explanation:To find the length of the rectangle, we can use the information given in the problem. Let's let the width be represented by W and the length be represented by L. We are told that the length is 26 feet more than the width, so we can write the equation L = W + 26. We are also given that the perimeter of the rectangle is 60 feet, so we can write the equation 60 = 2(W + L). We can substitute the value of L from the first equation into the second equation to solve for W. After finding the value of W, we can substitute it back into the first equation to find the value of L.
Let's start with the first equation: L = W + 26. Since we have an equation with two variables, we'll need to use the second equation to solve for the variables. Let's substitute the value of L in the second equation: 60 = 2(W + (W + 26)). We can simplify this equation by combining like terms: 60 = 2(2W + 26). We can distribute the 2 to the terms inside the parentheses: 60 = 4W + 52. We can then subtract 52 from both sides of the equation: 8 = 4W. Finally, we can divide both sides of the equation by 4 to solve for W: W = 2.
Now that we have the value of W, we can substitute it back into the first equation L = W + 26. This gives us: L = 2 + 26. We can simplify this equation to find that L = 28.
what is the twin prime conjecture?
Answer:
It is a prime number which is either 2 less or 2 more than another prime number
Step-by-step explanation:
Final answer:
The twin prime conjecture posits the existence of an infinite number of twin prime pairs, which are pairs of prime numbers that are two units apart.
Explanation:
The twin prime conjecture is an unsolved question in mathematics that relates to the distribution of prime numbers. It specifically addresses the existence of pairs of primes that are only two numbers apart, such as (11, 13), (17, 19), and (41, 43), which are known as twin primes. The conjecture proposes that there are an infinite number of these twin prime pairs, even though prime numbers themselves become less frequent as numbers increase. Despite many efforts, a definitive proof of this conjecture has not yet been found.
please answer this, and HURRY I am giving away 20points.
Question: What is the measure of angle DBA?
____Degrees
Answer:
132
Step-by-step explanation:
65+67=132 || 180-132=48 || 180-48=132
Answer:
132 Degrees.
Step-by-step explanation:
The interior of any triangle is 180 degrees.
Solve for angle DBC
65 + 67 = 132
180 - 132 = 48 degrees
Since the sum of DBA and DBC is 180, and we already know what 180 - 48 is, there you have it.
Mark is in training for a marathon race. He has been training by running 10 miles each day. He will
be increasing his running by this weekly formula: y = 10 (1.1), where y is the number of miles he
will run each day, x weeks from now.
What is the value of y if x = 0?
Round to the nearest mile.
Answer:
For x = 0, the value of y will be 10 miles.
Step-by-step explanation:
Mark is in training for a marathon race. Each day he runs 10 miles for this training purpose. He will be increasing his running by this weekly formula: [tex]y = 10(1.1)^{x}[/tex], where y is the number of miles he will run each day, x represents the number of weeks from now.
Now, for x = 0, the value of y will be [tex]y = 10(1.1)^{0} = 10[/tex] miles. (Answer)
Answer:
The Value of y is 10
Step-by-step explanation:
What is
2x-3y=-19
4x+3y=7
URGENT
Solve by elimination.
2x-3y=-19
+(4x+3y=7)
-----------------
6x=-12
x=-2
2(-2)-3y=-19
-3y=-15
y=5
Intersection Point: (-2,5)
What is the approximate area of the shaded sector in the circle shown below?
Step-by-step explanation:
[tex]area \: of \: sector = \frac{ \theta}{360 \degree} \times \pi {r}^{2} \\ \\ = \frac{110\degree}{360\degree} \times 3.14 \times {(16)}^{2} \\ \\ = \frac{110\degree}{360\degree} \times 3.14 \times 256 \\ \\ = \frac{88,422.4}{360} \\ \\ = 245.617778 \\ \\ \approx245.62 \: {in}^{2} [/tex]
a population of 800 cheetahs decreased by 13% per year. How many cheetahs will there be in the population after 5 years?
Answer:
399
Step-by-step explanation:
The population of a species of fish in a river increased by a factor of 1.05 every day for the amount of days shown in the graph. The function shows the number of fish in the river f(x) after x days:
f(x) = 100(1.05)x
Answer: C: 0 < x < 31
Step-by-step explanation: Because the < sign shows the line is going up towards the top. It starts from 0 and travels to the top-right to 31
A reasonable domain for this function to have would be 0 ≤ x ≤ 31.
How to solve for the domain of the functionWe have f(x) as the number of fishes that are present in this water. The month is October and October has 31 days.
The x values is the maximum of the number of days in October. The minimum value is given as 0 because it is the population in the beginning of the month.
Hence we have 0 ≤ x ≤ 31
Complete questionWhich of the following is a reasonable domain for the function?
0 ≤ x ≤ 100
0 ≤ x ≤ 31
All positive integers greater than 100
All positive integers less than 100
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prove the identity cos(x-y)-cos(x+y)=2sinx siny
Answer:
see explanation
Step-by-step explanation:
Using the Addition/ Subtraction formulae for cosine
Consider the left side
cos(x - y) - cos(x + y)
= cosxcosy + sinxsiny - (cosxcosy - sinxsiny) ← distribute
= cosxcosy + sinxsiny - cosxcosy + sinxsiny ← collect like terms
= 2sinxsiny = right side ⇒ proven
Can someone please answer this question please please answer it correctly and please show work answer 28 and 33 please
Answer:
Step-by-step explanation:
Answer:
28) B
33) D
Step-by-step explanation:
28) Numbers on the dice
1, 2, 3, 4, 5, 6
Numbers greater than 4
5, 6
There are 2 possibilities of rolling a number greater than 4 on the cube
2 numbers greater than 4 / Total amount of numbers
2/6 = 1/3
There is a 1/3 chance of rolling a number greater than 4
If the cube is tossed 120 times, about 1/3 of the time the number will be greater than 4
120 (1/3) = 120/1 * 1/3 = 120/3 = 40
The best estimate is 40 times, B
33)
These are all of the possibilities:
W - shaded
W - unshaded
X - shaded
X - unshaded
Y - shaded
Y - unshaded
Z - shaded
Z - unshaded
The answer that corresponds with all of these possibilities is D
Hope this helps :)
Find two nontrivial functions f(x) and g(x) so that f(g(x)) = (-6-3x)^6
Two nontrivial functions f(x) and g(x) that satisfy the equation f(g(x)) = (-6-3x)^6 are f(x) = x^6 and g(x) = -6 - 3x. These functions were found by assigning the inner function to g(x) and the outer function to f(x).
Explanation:Looking at the expression [tex]f(g(x)) = (-6-3x)^6[/tex], we can see that it is a composition of two functions. A possible way to choose the functions f(x) and g(x) is to let g(x) be the inner function and f(x) be the outer function.
Let's choose g(x) = -6 - 3x. This function linearly transforms the input x. Now, let's choose the function [tex]f(x) = x^6[/tex]. This function takes any input (including results from the g(x) function) and raises it to the power of 6.
So, when we apply g to x (g(x)) and then f to the result (f(g(x))), we get the original equation[tex]f(g(x)) = (-6-3x)^6[/tex]. Therefore, the two nontrivial functions f(x) and g(x) that satisfy the equation are f(x) = x^6 and g(x) = -6 - 3x.
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Which of the following is a solution to this inequality? y>1/2x+2
A. (1,4)
B. (-1,1)
C. (2,3)
D. (0,2)
None of the given points are solutions to the inequality.
Explanation:To determine which of the given points is a solution to the inequality y > 1/2x + 2, you need to substitute the coordinates of each point into the inequality and check if the inequality holds true.
Let's start with point (1, 4):
4 > 1/2 * 1 + 2
4 > 1/2 + 2
4 > 2.5 + 2
4 > 4.5
The inequality does not hold, so point (1, 4) is not a solution to the inequality.
Now, let's try point (-1, 1):
1 > 1/2 * -1 + 2
1 > -1/2 + 2
1 > 1.5
The inequality does not hold, so point (-1, 1) is not a solution to the inequality.
Similarly, checking for points (2, 3) and (0, 2), we find that neither of them satisfy the inequality.
Therefore, none of the given points, (1, 4), (-1, 1), (2, 3), or (0, 2), are solutions to the inequality y > 1/2x + 2.
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which expression is equivalent to 3/27x18?
a.3x3
b.3x6
c.9x3
d.9x6
Answer:
the answer is B
Step-by-step explanation:
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0.230769231 as a fraction
Final answer:
To express 0.230769231 as a fraction, the numerator is 230769231 and the denominator is 10^9.
Explanation:
To express the decimal 0.230769231 as a fraction, we need to determine the numerator and denominator. The numerator is the decimal without the decimal point, which is 230769231. The denominator is based on the number of decimal places, which is 9 because there are 9 digits in the decimal part. Therefore, the fraction is 230769231/10^9.