Answer:
450
Step-by-step explanation:
5% of 300 = 15
300+10(15)=450
Using the compound interest formula, if you deposit $300 in an account earning 5% interest compounded annually, you would have approximately $488.85 in the account after 10 years.
Explanation:This problem involves compound interest, which appeal to financial maths. The formula for compound interest is A = P*(1 + r/n)^(nt), where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money).r is the annual interest rate (in decimal).n is the number of times that interest is compounded per year.t is the time the money is invested for, in years.For this problem, P = $300, r = 5% or 0.05, n = 1 (because it's compounded annually), and t = 10 years. Substituting these values into the formula, you have A = 300*(1 + 0.05/1)^(1*10).
Doing the math, A = $300 * (1.05)^10 ≈ $488.85. So after 10 years, you would have approximately $488.85 in the account.
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When you are looking at used cars, you should only look at local lots and newspapers
True
False
Please don't ask me what a true/false question has to do with math, but...
Answer:
The statement is false.
Step-by-step explanation:
When you are looking at used cars, you should only look at local lots and newspapers - This statement is false.
When you are buying a used car, you should look not only in the local lots and newspapers but also online ans various used cars websites.
You can also personally visit the used car market to get wide range of cars and various comparative prices.
Kim kept track of how much cereal she ate for 2 months and found that she ate 256 ounces of cereal in that time. How many pounds is that? (16 ounces = 1 pound)
Answer:
16 pounds
Step-by-step explanation:
Total cereal she ate = 256 ounces
How many pounds she ate = ?
Given that (16 ounces = 1 pound)
Therefore, we have to divide the total ounces by 16 to calculate the cereal she ate in pounds = 256/16 = 16 pounds
Answer:
A. 16
Step-by-step explanation:
What is measure of angle R?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
°
P Q R is a right triangle. Q is a right angle. P Q is equal to five centimeters, Q R is equal to twelve centimeters and P R is equal to thirteen centimeters.
Answer:
The measure of angle R is [tex]22.62\°[/tex]
Step-by-step explanation:
we know that
In the right triangle PQR
The cosine of angle R is equal to divide the adjacent side angle R by the hypotenuse
so
[tex]cos(R)=\frac{QR}{PR}[/tex]
substitute the values
[tex]cos(R)=\frac{12}{13}[/tex]
[tex]<R=arccos(\frac{12}{13})=22.62\°[/tex]
see the attached figure to better understand the problem
Write an equation for the nth term of the geometric sequence 3584, 896, 224... Find the sixth term of this sequence
Answer:
Step-by-step explanation:
r = [tex]\frac{a_n}{a_{n-1}} = \frac{896}{3584} = \frac{1}{4}[/tex]
Using the geometric series formula for the nth term:
[tex]S_n = a \cdot \frac{1-r^n}{1-r} => S_{6} = 3584 \cdot \frac{1 - (\frac{1}{4})^{6} }{1 - \frac{1}{4} } = 4777\frac{1}{2}[/tex]
Final answer:
The equation for the nth term of the geometric sequence is a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio. The sixth term of the sequence is 14.
Explanation:
The given sequence is a geometric sequence. In a geometric sequence, each term is found by multiplying the previous term by a common ratio. To find the equation for the nth term of the geometric sequence, we need to find the common ratio. We can do this by dividing any term in the sequence by the previous term.
For example, dividing the second term 896 by the first term 3584 gives us a common ratio of 1/4.
So, the equation for the nth term of the sequence is:
an = a1 × r(n-1)
where a1 is the first term and r is the common ratio.
To find the sixth term, we can substitute n = 6 into the equation:
a6 = 3584 × (1/4)(6-1)
a6 = 3584 × (1/4)5
a6 = 14
Find the area of a triangle when
Answer:
The area of the triangle = 31.5 feet² ⇒ answer (c)
Step-by-step explanation:
∵ Area of any Δ = 1/2 (side 1)(side 2)(sin the angle between them)
∴ The area of the Δ = 1/2 (b)(c) sin(∠A)
∵ b = 11 feet
∵ c = 10 feet
∵ m∠A = 35°
∴ Area of the Δ = 1/2 (11)(10) (sin(35)) = 31.547 feet²
∴ The area of the triangle = 31.5 feet²
∴ The answer is (c)
I need help with this. This is hard.
h = 12.
See the attached picture:
Please help me out!!!!!
Answer:
x = 22°Step-by-step explanation:
A diameter of a rhombus is an angle bisector. Therefore we have the equation:
[tex]3x-11^o=x+23^o[/tex] add 11° to both sides
[tex]3x=x+44^o[/tex] subtract x from both sides
[tex]2x=44^o[/tex] divide both sides by 2
[tex]x=22^o[/tex]
WHAT IS 11/6 simplified I CANT DO THIS MATH IT IS TOOOOO HARDDDDD JK IM JUST TO LAZY >:( thanks
Answer:
It can't be simplified.
!!!!!!!!!!!!!!!! HELP 25 points
What is the completely factored form of
x3 + 4x2 – 9x – 36?
(x + 3)(x – 3)
(x2 – 9)(x + 4)
(x + 3)(x – 3)(x + 4)
(x – 3)(x – 3)(x + 4)
x3 + 4x2 - 9x - 36
x2 (x + 4) - 9(x + 4)
(x2 - 9) (x + 4)
(x - 3) (x + 3) (x + 4)
Expand the following log:
[tex]log_{3} (x^{4} y)[/tex]
SHOW ALL WORK.
Answer:
[tex]\log_{3}(x^4y)=4\log_{3}(x)+\log_{3}(y)[/tex]
Step-by-step explanation:
The given logarithmic expression is
[tex]log_{3}(x^4y)[/tex]
Recall and use the product property of logarithm: [tex]\log_a(MN)=\log_a(M)+\log_a(N)[/tex];
This implies that;
[tex]\log_{3}(x^4y)=\log_{3}(x^4)+\log_{3}(y)[/tex]
Recall again that; [tex]\log_a(M^n)=n\log_a(M)[/tex];
We apply this property to get;
[tex]\log_{3}(x^4y)=4\log_{3}(x)+\log_{3}(y)[/tex]
Solving Rational Equations. LCD Method. Show work.
[tex]\frac{3}{5x} + \frac{7}{2x} =1[/tex]
Answer: [tex]x=\frac{41}{10}[/tex]
Step-by-step explanation:
Descompose the denominators into their prime factors to calculate the Least Common Denominator (LCD):
[tex]5x=5*x[/tex]
[tex]2=2*x[/tex]
Choose the common and non-common numbers and varibles with the largest exponents and multiply them:
[tex]LCD=5*2*x=10x[/tex]
Divide eac originl denominator by the LCD and multiply the resul by each numerator. Then, make the addition and solve for x:
[tex]\frac{3(2)+7(5)}{10x}=1\\\\\frac{6+35}{10x}=1\\\\\frac{41}{10x}=1\\\\41=10x\\x=\frac{41}{10}[/tex]
Answer:
[tex]x=4.1[/tex]
Step-by-step explanation:
The given equation is;
[tex]\frac{3}{5x}+\frac{7}{2x}=1[/tex]
Multiply through by the Least Common Denominator which is [tex]-10x[/tex]
[tex]10x(\frac{3}{5x})+10x(\frac{7}{2x})=10x[/tex]
Cancel the common factors to obtain;
[tex]2(3)+5(7)=10x[/tex]
[tex]6+35=10x[/tex]
[tex]41=10x[/tex]
Divide by 10
[tex]x=\frac{41}{10}[/tex]
[tex]x=4.1[/tex]
Use synthetic division to perform the indicate division. Write the poly nominal in the form p(x) = d(x)q(x) + r(x)
[tex](3x^{2} -2x+1)[/tex] ÷ [tex](x-1)[/tex]
A figure is translated using the rule (x, y) → (x – 3, y + 6). Which describes how the figure is moved?
A. left 3 units and down 6 units right
B. 3 units and down 6 units left
C. 6 units and down 3 units left
D. 3 units and up 6 units
Answer:
3 units to the right and 6 units upStep-by-step explanation:
f(x) + n - shift the graph of f(x) n units up → (x, y + n)
f(x) - n - shift the graph of f(x) n units down → (x, y - n)
f(x - n) - shift the graph of f(x) n units to the right → (x - n, y)
f(x + n) - shift the graph of f(x) n units to the left → (x + n, y)
===================================
(x, y) → (x - 3, y + 6)
x - 3 → shift the graph 3 units to the right
y + 6 → shift the graph 6 units up
Answer:
the right answer is left 3 units and up 6 units
Step-by-step explanation:
The calibration of a scale is to be checked by weighing a 10-kg test specimen 25 times. Suppose that the results of different weighings are independent of one another and that the weight on each trial is normally distributed with σ = .200 kg. Let µ denote the true average weight reading on the scale. (a) What hypotheses should be tested? (b) With the sample mean itself as the test statistic, what is the P-value when x = 9.85, and what would you conclude at significance level .01? (c) For a test with α = .01, what is the probability that recalibration is judged unnecessary when in fact µ = 10.2?
Answer:
a: That the mean weight of the trials is 10 kg
b: See attached photo for work
Step-by-step explanation:
We want to see if the scale is weighing properly and are using a 10 kg weight to calibrate it. That means our hypothesis test is that the mean weight of the trails (in this case 25) is 10 kg.
The hypothesis we will use are
H0: µ = 10
Ha: µ ≠ 10
The alternate hypothesis has a not equals to sign because if the scale weighs too much or to little, then it needs to be better calibrated, so it's a two tailed test.
The calibration of the scale follows a normal distribution.
The null and the alternate hypotheses are: [tex]\mathbf{H_o: \mu = 10}[/tex] and [tex]\mathbf{H_a: \mu \ne 10}[/tex]The p-value when [tex]\mathbf{\bar x = 9.85}[/tex] is [tex]\mathbf{p=0.000494}[/tex]The scale needs to be calibratedThe probability that recalibration is judged unnecessary is less than 0.00001The given parameters are:
[tex]\mathbf{\sigma = 0.200}[/tex]
[tex]\mathbf{\mu = 10}[/tex]
[tex]\mathbf{n = 25}[/tex]
[tex]\mathbf{\bar x = 9.85}[/tex]
(a) The null and the alternate hypotheses
The true average weight is to be tested.
So, the null and the alternate hypotheses are:
[tex]\mathbf{H_o: \mu = 10}[/tex]
[tex]\mathbf{H_a: \mu \ne 10}[/tex]
(b) The p-value when [tex]\mathbf{\bar x = 9.85}[/tex]
First, we calculate the test statistic
[tex]\mathbf{t = \frac{\bar x - \mu}{\sigma/\sqrt n}}[/tex]
So, we have:
[tex]\mathbf{t = \frac{9.85 - 10}{0.2/\sqrt{25}}}[/tex]
[tex]\mathbf{t = \frac{9.85 - 10}{0.2/5}}[/tex]
[tex]\mathbf{t = \frac{-0.15}{0.04}}[/tex]
[tex]\mathbf{t = -3.75}[/tex]
Using p-value calculator, we have:
[tex]\mathbf{p=0.000494}[/tex]
The critical regions of [tex]\mathbf{t = -3.75}[/tex] are t >2.797 and t < -2.797
Because -3.75 < -2.797, we reject the null hypothesis.
This means that, the scale needs to be calibrated
(c) Probability that recalibration is judged when [tex]\mathbf{\mu = 10.2}[/tex]
First, we calculate the test statistic
[tex]\mathbf{t = \frac{\bar x - \mu}{\sigma/\sqrt n}}[/tex]
So, we have:
[tex]\mathbf{t = \frac{9.85 - 10.2}{0.2/\sqrt{25}}}[/tex]
[tex]\mathbf{t = \frac{-0.35}{0.04}}[/tex]
[tex]\mathbf{t = -8.75}[/tex]
Using p-value calculator, we have:
[tex]\mathbf{p<0.00001}[/tex]
The probability that recalibration is judged unnecessary is less than 0.00001
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Linda saves $1.55 every day. Tyron saves $3.90 every day. Linda started saving 3 days earlier than Tyron. On which day will Tyron's savings be more than Linda's savings?
To determine when Tyron's savings will surpass Linda's, we can set up an inequality using their daily saving rates and the fact that Linda started 3 days earlier. Solving for the number of days Tyron needs to save, we find that Tyron will surpass Linda's savings after saving for 2 full days.
Linda and Tyron are saving money on a daily basis, but Linda started saving 3 days earlier than Tyron. To find out on which day Tyron's savings will be more than Linda's, we need to set up an equation.
Let's define x as the number of days after which Tyron starts saving. Since Linda starts 3 days earlier, she has been saving for x + 3 days by the time Tyron starts saving.
Linda's daily savings: $1.55
Tyron's daily savings: $3.90
Linda's total savings after x + 3 days: $1.55(x + 3)
Tyron's total savings after x days: $3.90x
We want to find the value of x at which Tyron's total savings exceed Linda's, so we set up the inequality:
$3.90x > $1.55(x + 3)
Now, solve for x:
$3.90x > $1.55x + $4.65
$3.90x - $1.55x > $4.65
$2.35x > $4.65
x > $4.65 / $2.35
x > 1.978
Since x represents the number of days and we cannot have a fraction of a day in this context, x must be at least 2 days. Therefore, Tyron's savings will be more than Linda's after he has saved for 2 days.
If I got 12 baseball cards on monday 24 on tuesday and gave some to my brother and had 13 baseball cards left, how many did I give to my brother?
Answer:
23 Cards were given to your brother.
Step-by-step explanation:
12 + 24 = 36
36 - 13 = 23
Answer:
you gave him 23 cards
Step-by-step explanation:
12+24=36, 36-13=23
What is the solution to this system of linear equations?
7x - 2y = -6
8x + y = 3
A.(-6,3)
B.(0,3)
C.(1,-5)
D.(15,-1)
Answer:
B. (0, 3)
Step-by-step explanation:
Trying the offered solutions in the given equations gets you there pretty quickly.
7·(-6) -2(3) ≠ -6 . . . eliminates choice A
__
7·0 -2·3 = -6
8·0 +3 = 3 . . . . . . . choice B is the solution
Answer:
(0,3)
B is correct
Step-by-step explanation:
Given: The system of equation.
[tex]7x-2y=-6[/tex]
[tex]8x+y=3[/tex]
Now, we solve for x and y using elimination method.
Elimination method: In this method to make the coefficient of one variable same and then cancel out by addition of both equation.
Multiply 2nd equation by 2 and we get
[tex]16x+2y=6[/tex]
[tex]7x-2y=-6[/tex]
Add both equation and eliminate y
[tex]23x=0[/tex]
[tex]x=0[/tex]
Put x=0 into 1st equation, 7x-2y=-6
7(0) - 2y = -6
y = 3
Solution: x = 0 and y = 3
Hence, The solution of the equation would be (0,3)
There are 888 employees on The Game Shop's sales team. Last month, they sold a total of ggg games. One of the sales team members, Chris, sold 171717 fewer games than what the team averaged per employee. How many games did Chris sell?
Answer:
[tex]\frac{g}{8}-17[/tex] games
Step-by-step explanation:
Employees: 8
Sales last month: g
Average: [tex]\frac{totalGames}{Employees}[/tex]
To find out how many games Chris sold, we have to take the average and subtract 17.
[tex]\frac{g}{8}-17[/tex]
Since there are no more values we can use, this is as simple as we can get it. If we knew how many games they sold last month, we could get an exact answer for Chris using this expression.
Answer:
g over 8 -17
Step-by-step explanation:
Consider the infinite geometric series ∑∞ n=1 -4(1/3)^n-1
a. Write the first four terms of the series.
b. Does the series diverge or converge.
c. If the series has a sum, find the sum.
a. The series is
[tex]\displaystyle\sum_{n=1}^\infty-4\left(\frac13\right)^{n-1}=-4-\frac43-\frac4{3^2}-\frac4{3^3}-\cdots[/tex]
(first four terms are listed)
b. The series converges because this is a geometric series with [tex]r=\dfrac13<1[/tex].
c. Let [tex]S_N[/tex] be the [tex]N[/tex]-th partial sum of the series:
[tex]S_N=\displaystyle\sum_{n=1}^N-4\left(\frac13\right)^{n-1}[/tex]
[tex]S_N=-4-\dfrac43-\dfrac4{3^2}-\cdots-\dfrac4{3^{N-1}}[/tex]
Multiplying both sides by [tex]\dfrac13[/tex] gives
[tex]\dfrac13S_N=-\dfrac43-\dfrac4{3^2}-\dfrac4{3^3}-\cdots-\dfrac4{3^N}[/tex]
Subtracting this from [tex]S_N[/tex] gives
[tex]S_N-\dfrac13S_N=\dfrac23S_N=-4+\dfrac4{3^N}[/tex]
[tex]\implies S_N=-6+\dfrac6{3^N}[/tex]
As [tex]N[/tex] gets larger and larger [tex](N\to\infty)[/tex] the rational term converges to 0 and we're left with
[tex]\displaystyle\lim_{N\to\infty}S_N=\sum_{n=1}^\infty-4\left(\frac13\right)^{n-1}=-6[/tex]
Using he equation 12(x-3.20)=54 , carolyn determines that she will make a profit of $7.70 on each necklace. Which error did carolyn make?
Answer:
This is correct, Carolyn will make $7.70 for each necklace but she loses $3.20 most likely for the suplices for the making of the necklace so she really earns $4.50.
Step-by-step explanation:
The ratio of boys to girls in Ella's grade is 3/4 the ratio of boys to girls in minhs grade is 4 to 5 each grade has a total of 20 girls how many boys are in each grade
Answer:
Ella's Grade: 15
Minh's Grade: 16
Step-by-step explanation:
If each grade has 20 girls in the grade, then that implies effectively that the ratios would apply via fractions, which are 3:4 and 4:5. As such, take both Fractions and increase them both to 20: 15:20 and 16:20.
The number of boys in Ella's grade is 15 and Minh's grade is 16
Given that,
The ratio of boys to girls in Ella's grade is 3:4
And the ratio of boys to girls in Minh's grade is 4:5
The total number of girls is 20
Computation:
Let the number of boys be [tex]x[/tex]
So in the case of Ella's,
[tex]\frac{3}{4}=\frac{x}{20}\\x=\frac{20\times3}{4}\\x=15[/tex]
And in case of Minh's,
[tex]\frac{4}{5}=\frac{x}{20}\\x=\frac{20\times4}{5}\\x=16[/tex]
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Find three solutions of the equation.
y = –8x
(0, 0), (–3, 22), (–2, 16)
(3, –24), (0, 0), (–1, 9)
(–2, 16), (3, –24), (–4, 32)
(–2, 16), (3, –24), (2, –17)
Answer:
3rd group of possible answers is the correct set
Step-by-step explanation:
Each of the three points in the 3rd line of possible answers is a solution of the given equation, as can be verified by substitution:
If x = -2, y = -8(-2) = +16
If x = 3, y = -8(3) = -24
If x = -4, y = -8(-4) = +32
Answer:
c
Step-by-step explanation:
Which of the following is true about a function that is constant?
It is a horizontal line.
It moves in an upward direction.
It moves in a downward direction.
It is a curve.
HELP ME PLZZZZZZZZZZZZZZZZZZZZZ
Graph of constant function is a horizontal line
It’s a horizontal line because all of the x’s must be different
Find sin and tan (Picture provided)
Answer:
Option C. [tex]sin(\theta)=-\frac{\sqrt{33}}{7}[/tex] , [tex]tan(\theta)=-\frac{\sqrt{33}}{4}[/tex]
Step-by-step explanation:
we know that
If cosine of angle theta is positive then angle theta belong to the I or IV quadrant
and
If co secant of angle theta is negative then angle theta belong to the III or IV quadrant
therefore
angle theta belong to the IV quadrant (common solution)
Part 1) Find [tex]sin(\theta)[/tex]
we know that
[tex]sin^{2} (\theta)+cos^{2} (\theta)=1[/tex]
we have
[tex]cos(\theta)=4/7[/tex]
substitute the value
[tex]sin^{2}(\theta)=1-(4/7)^{2}[/tex]
[tex]sin^{2}(\theta)=1-(16/49)[/tex]
[tex]sin^{2}(\theta)=(33/49)[/tex]
[tex]sin(\theta)=-\frac{\sqrt{33}}{7}[/tex] ----> is negative because the angle belong to the IV quadrant
Part 2) Find [tex]tan(\theta)[/tex]
we know that
[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]
we have
[tex]sin(\theta)=-\frac{\sqrt{33}}{7}[/tex]
[tex]cos(\theta)=4/7[/tex]
substitute the values
[tex]tan(\theta)=\frac{-\frac{\sqrt{33}}{7}}{4/7}[/tex]
[tex]tan(\theta)=-\frac{\sqrt{33}}{4}[/tex]
Point M is located between X and Y on this number line.
<-----x-------------y----->
-4 -2 0 2 4 6 8
( -2 is X and 6 is Y )
Which number could not be the coordinate of point M?
a- √48
b- √18
c- √35
d- √27
Answer:
√48 could not be M.
Step-by-step explanation:
M must be between - 2 and 6, so:
a. √48 = 6.93 so this can't be M.
b. √18 = 4.24 so this could be M.
c and d could also be M.
The coordinate of point M can be any of the given options.
Explanation:To determine the possible coordinates of point M, we need to find the values between X (-2) and Y (6) on the number line provided. Starting from X (-2) and moving towards Y (6), the numbers that lie between them are -2, 0, 2, 4, and 6. We can see that all the given options for the coordinate of point M can be found on the number line. Therefore, none of the given numbers could not be the coordinate of point M.
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6x^2-66x+144=0 solving quadratic equation
Factor out the common term 6
6(x^2 - 11x + 24) = 0
Factor x^2 - 11x + 24
6(x - 8)(x - 3) = 0
Solve for x;
x = 8,3
simplify the trigonometric expression. show your work
See the attached picture for the solution:
Answer:
Step-by-step explanation:
1/(1+sinθ) + 1/(1-sinθ)
= (1-sinθ)/[(1+sinθ)(1-sinθ)] + (1+sinθ)/[(1-sinθ)(1+sinθ)]
= [(1-sinθ) + (1+sinθ)] / [(1-sinθ)(1+sinθ)]
= [1 - sinθ + 1 + sinθ] / [1 - sin^2sθ]
= 2 / cos^2θ
Explain how the number of edges for the rectangular prison compares to the number of edges for the unit cube
Answer:
Step-by-step explanation:
A rectangular prism has 12 edges. In geometry, a prism is a solid figure with parallel ends or bases that are the same size and shape, with each side representing a parallelogram. The parallelograms in a rectangular prism are all rectangles.
The rectangular prism also has six faces, or flat sides. The surface area of a rectangular prism is determined by multiplying the length by the width of each of the six rectangles and by then adding the products together.
Find the length of segment BA.
A) 163.3
B) 128.6
C) 84.7
D) 59.8
Answer:
D) 59.8
Step-by-step explanation:
m<B = 120 deg
Since we know the measure of an angle and the length of the opposite side, we can establish the ratio of the law of sines, so we use the law of sines to find the length of side BA.
[tex] \dfrac{\sin A}{a} = \dfrac{\sin B}{b} = \dfrac{\sin C}{c} [/tex]
[tex] \dfrac{\sin A}{BC} = \dfrac{\sin B}{AC} = \dfrac{\sin C}{AB} [/tex]
[tex] \dfrac{\sin B}{AC} = \dfrac{\sin C}{AB} [/tex]
[tex] \dfrac{\sin 120^\circ}{200} = \dfrac{\sin 15^\circ}{AB} [/tex]
[tex] \dfrac{\sin 120^\circ}{200} = \dfrac{\sin 15^\circ}{AB} [/tex]
[tex] (AB)\sin 120^\circ = 200 \sin 15^\circ [/tex]
[tex] AB = \dfrac{200 \sin 15^\circ}{\sin 120^\circ} [/tex]
[tex] AB = 59.8 [/tex]
There are two large pieces of construction paper. The red piece has an area of 90 inches squared , while the blue piece is 12 inches wide. Which paper is larger?
Answer:
You cant solve this without one more number.
Step-by-step explanation:
You need the length of the blue piece because it could be smaller or larger at this point. I may be wrong but unless I am missing something, and I totally might be if this is a kind of math I've never done, then please feel free to ignore me :) and have a lovely day!