If Gloria deposited $500 into a bank account that earned 7.5% simple interest each year and she earned $225 in interest before closing the account, then the number of years that the money in the account is 6 years
The deposited amount = $500
The simple interest = 7.5%
The interest she earned = $225
Then the final amount = The deposited amount + The interest she earned
= 500+225
= $725
The equation of simple interest
A = P(1+rt)
Where A is the final amount
P is the initial amount
r is the interest rate
t is the time period
725 = 500(1+(7.5/100)×t)
(1+0.075t) = 1.45
0.075t = 0.45
t = 0.45/0.075
t = 6 years
Hence, if Gloria deposited $500 into a bank account that earned 7.5% simple interest each year and she earned $225 in interest before closing the account, then the number of years that the money in the account is 6 years
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4. Find the value of p if 2P=2^2 p-7
Answer:
P = 7
Step-by-step explanation:
[tex]{ \tt{ {2}^{p} = {2}^{2p - 7} }} \\ [/tex]
- From the law of indices; If an index has same base, then the powers are equal.
[tex]{ \boxed{ \rm{ \blue{ ({x}^{a} = {x}^{b}) \rightarrow{ \red{a = b}} }}}}[/tex]
[tex]{ \tt{p = 2p - 7}} \\ { \tt{p -2 p = - 7}} \\ { \tt{p = 7}}[/tex]
OR:
Applying logarithms can also be borrowed;
[tex]{ \tt{ log( {2}^{p} ) = log( {2}^{2p - 7} ) }} \\ \\ { \tt{p log(2) = (2p - 7) log(2) }} \\ \\ { \tt{ \frac{p log(2) }{ log(2) } = \frac{(2p - 7) log(2) }{ log(2) } }} \\ \\ { \tt{p = 2p - 7}} \\ \\ { \tt{p - 2p = - 7}} \\ \\ { \tt{p = 7}}[/tex]
Choose if each statement is True or False.
{(2, 2), (3, 2), (4, 2), (6, 2)} is a function:
{(-1, 5), (0, 8), (3, 12), (6, 21)} is a function:
Answer:
The first one in red is a function. The second one in blue is not a function.
Step-by-step explanation:
Using the vertical line test, if you were to draw a vertical line and move the line from left to right, it should not have two points of intersection (if the vertical line intersects the relation more than one, then the relation is not a function).
solve step through stepx + 2y = 83x - 2y = 0
Add both the equations
[tex]\begin{gathered} x+2y=8 \\ 3x-2y=0 \\ \text{Add left hand side terms together and right hand side terms together.} \\ x+2y+3x-2y=8+0 \\ 4x=8 \\ x=\frac{8}{4}=2 \end{gathered}[/tex]Substitute 2 for x in x+2y =8 to find y
[tex]\begin{gathered} 2+2y=8 \\ 2y=8-2 \\ 2y=6 \\ y=\frac{6}{2}=3 \end{gathered}[/tex]The solutions to the equations are x=2 and y=3.
Hello, I need help with this practice problem, thank you!
In order to find the distance between the given points, use the following formula:
[tex]d=\sqrt[]{(x_2-x_1_{}^{})^2+(y_2-y_1)^2}[/tex]where (x1,y1) and (x2,y2) are the coordinates of the points.
In this case, you have:
(x1,y1) = K(1,-1)
(x2,y2) = F(6,-9)
Replace the previous values of the parameters into the formula for d and simplify:
[tex]\begin{gathered} d=\sqrt[]{(6-1)^2+(-9-(-1))^2} \\ d=\sqrt[]{(5)^2+(-9+1)^2} \\ d=\sqrt[]{25+(-8)^2}=\sqrt[]{25+64} \\ d=\sqrt[]{89} \end{gathered}[/tex]Hence, the distance between K and F points is √89.
Solve the inequality for x and identify the graph of its solution. 4[x+ 2] < 8
Answer:
x < 0
Step-by-step explanation:
4(x + 2) < 8
4x + 8 < 8
4x < 0
x < 0
◀━━━━━|──>
0
What is the GCF of 12 and 24
Answer:
12
Step-by-step explanation:
The GCF of 12 and 24 is 12. To calculate the most significant common factor of 12 and 24, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; characteristics of 24 = 1, 2, 3, 4, 6, 8, 12, 24) and choose the most significant factor that exactly divides both 12 and 24, i.e., 12.
Jessica has a barrel to fill with water. The barrel is 24 inches high with a radius of 12 inches. She is using a cup to fill the the barrel. The cup has a height of 6 inches and diameter of 4 inches. How many full cups will she need in order to fill the barrel?
SOLUTION.
The barrel and the cub are both cylinders. To find how many cups that will fill the barrel, we find the volumes of both the cup and the barrel and divide that of the barrel by the cup
Volume of a cylinder is given as
[tex]\begin{gathered} \text{Volume = }\pi r^2h,\text{ r is radius and h is height of the cylinder } \\ radius\text{ of the barrel = }12,\text{ height = 24} \\ \text{Volume of barrel = }\pi r^2h \\ \text{Volume of barrel = 3.14}\times12^2\times24 \\ \text{Volume of barrel = }10851.84inch^3 \end{gathered}[/tex]Volume of the cub becomes
[tex]\begin{gathered} \text{radius of cup = }\frac{4}{2}=2 \\ \text{Volume of barrel = }\pi r^2h \\ \text{Volume of cup = }3.14\times2^2\times6 \\ \text{Volume of cup = }75.36inches^3 \end{gathered}[/tex]Number of cups become
[tex]\frac{10851.84}{75.36}\text{ = 144 cups }[/tex]A Gallup poll conducted in November of 2011 asked the following question, "What would you
say is the most urgent health problem facing this country at the present time?" The choices
were access, cost, obesity, cancer, government interference, or the flu. The responses were
access (27%), cost (20%), obesity (14%), cancer (13%), government interference (3%), or the
flu (less than 0.5%).
The following is an excerpt from the Survey Methods section. "Results for this Gallup poll are based on telephone interviews conducted Nov. 3-6, 2011, with a random sample of 1,012
adults ages 18 and older, living in all 50 U.S. states and the District of Columbia. For results
based on a total sample of national adults, one can say with 95% confidence that the maximum margin of sampling error is ±4 percentage points."
Based on this poll, we are 95% confident that between_____% and ______% of U.S. adults feel that access to health care is the most urgent health-related problem.
(Enter numbers only. Do not include the %, e.g. enter 50 not 50%)
Based on this poll, we are 95% confident that between 23% (lower limit) and 31% (upper limit) of U.S. adults feel that access to health care is the most urgent health-related problem.
How do we determine the lower and upper limits for the confidence level?The lower limit is the lowest percentage of poll participants who choose access to health care as the most urgent health-related problem.
The upper limit is to the highest percentage of poll participants who choose access to health care as the most urgent health-related problem.
Using the lower and upper limits, the Gallup poll can confidently estimate the range of the poll participants who pin-pointed access to health care as the most urgent.
Mean responses who choose access = 27%
Margin of error = ±4
Lower Limit = µ - margin of error
= 27% - 4%
=23%
Upper Limit = µ + margin of error
= 27% + 4%
=31%
Thus, at a 95% confidence level, the Gallup poll can claim that 27% ±4% of poll participants rated access to health care as the most urgent issue.
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Find the equation of the line that passes through the given point and has the given slope. (Use x as your variable.)(4, −3), m = −2
General equation of line:
[tex]y=mx+c[/tex]Where,
[tex]\begin{gathered} m=\text{slope} \\ c=y-\text{intercept} \\ (x,y)=(4,-3) \end{gathered}[/tex]Slope of line is -2 then:
[tex]\begin{gathered} y=mx+c \\ y=-2x+c \end{gathered}[/tex][tex](x,y)=(4,-3)[/tex][tex]\begin{gathered} y=-2x+c \\ -3=-2(4)+c \\ -3=-8+c \\ 8-3=c \\ 5=c \end{gathered}[/tex][tex]\begin{gathered} y=mx+c \\ y=-2x+5 \end{gathered}[/tex]Equation of line is y=-2x+5
Beginning with the general form of a quadratic equation. ax^2+bx+c=0, solve for x by using the completing the square method, thus deriving the quadratic formula. To earn full credit be sure to show all steps/calculations. You may want to do the work by hand and upload a picture of that written work rather than try to type it out.
to solve ax^2 + bx + c = 0 using completing the square method
divide all terms by a so as to reduce the coefficient of x^2 to 1
x^2 + bx/a + c/a = 0
subtract the constant term from both sides of the equation
x^2 + bx/a = -c/a
to have a square on the left sie the third term (constant) should be
(b/2a)^2
so add that amount to both side
x^2 + bx/a + (b/2a)^2 = (b/2a)^2 - c/a
rewrite the left side as a square
(x + (b/2a))^2 = (b/2a) - c/a
take the square root of both sides
x + (b/2a) = + square root of (b/2a)^2 - c/a
subtract the constant term on the left side from both sides
[tex]\begin{gathered} x\text{ = }\pm\sqrt[]{(\frac{b}{2a}})^2\text{ - c/a - (b/2a)} \\ x\text{ = -b }\pm\sqrt[]{\frac{b^2\text{ - 4ac}}{2a}} \end{gathered}[/tex]Please help and round to the nearest minute if needed
Solution
For this case we have the following angle:
30 1/6 º
and then we need to convert to degrees and minutes so we can do this:
1 º= 60 min
then 1/6º* (60min/ 1º)= 10 min
Then the answer is:
30º 60'
Answer the following Formula:[tex]5 \times 5 \times 6 \times 8 - 6 \times 9 \times 524 \times 8 \times 6 + 9 - 725 \times 6[/tex]
we have the expression
[tex]5\times5\times6\times8-6\times9\times524\times8\times6+9-725\times6[/tex]we know that
Applying PEMDAS
P ----> Parentheses first
E -----> Exponents (Powers and Square Roots, etc.)
MD ----> Multiplication and Division (left-to-right)
AS ----> Addition and Subtraction (left-to-right)
solve Multiplication First
5x5x6x8=1,200
9x524x8x6=226,368
725x6=4,350
substitute
1,200-6x226,368+9-4,350
solve
6x226,368=1,358,208
1,200-1,358,208+9-4,350
Solve the addition and subtraction
1,200-1,358,208+9-4,350=-1,361,349
answer is-1,361,349given the equation 7x + 3 = 7X - _______ , what's would go in the blank to make each of the following true:so the equation is true for no values of xso the equation is true for all values of xso the equation is true for only one value of x
Let k be the number in the blank, so that:
[tex]7x+3=7x-k[/tex]Substract 7x from both sides:
[tex]3=-k[/tex]These two equations are equivalent regardless the value of x. We can change the conclusions that we may obtain by choosing different values for k.
Then, the equation:
[tex]7x+3=7x-0[/tex]Is true for no values of x.
If we want the equation to be false regardless of the value of x, then set k so that -k is different from 3. For example, set k=0:
[tex]\begin{gathered} 3=-0 \\ \Rightarrow3=0 \end{gathered}[/tex]Since this is contradictory, then there are no values of x that make the equation true.
If we want the equation to be true for all values of x, then 3=-k must be an identity. Then, let k=-3:
[tex]\begin{gathered} 3=-(-3) \\ \Rightarrow3=3 \end{gathered}[/tex]Then, the equation:
[tex]7x+3=7x-(-3)[/tex]Is true for all values of x.
If we want the equation to be true for only one value of x, we have to bring back x into the equation 3=-k. So, we can take k=x. This way, we would have:
[tex]\begin{gathered} 7x+3=7x-x \\ \Rightarrow3=-x \\ \Rightarrow x=-3 \end{gathered}[/tex](12-1) (-2-3) slope p l z
[tex]m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{ - 3 - ( - 1)}{ - 2 - 12} \\ m = \frac{ - 3 + 1}{ - 14} \\ m = \frac{ - 2}{ - 14} \\ m = \frac{1}{7} [/tex]
ATTACHED IS THE SOLUTION..I also provided you with the formula used to get the gradient.
John purchased 4
apples for $1.25
each and 1 orange
for 2.49 How
much does he
spend in all?
Answer:
$7.49
Step-by-step explanation:
$1.25 x 4 = $5
1 x $2.49 = $2.49
5 + 2.49 = $7.49
given the following trig equations find the exact value of the remaining five trig functions.cos0 = 4/9 where sin0 < 0( sin, tan, csc, cot, sec)
we have that:
[tex]\sin ^2\theta=1-\cos ^2\theta=1-\frac{16}{81}=\frac{65}{81}\rightarrow\sin \theta=-\frac{\sqrt[]{65}}{9}[/tex]having this we get that
[tex]\tan \theta=\frac{-\sqrt[]{65}}{4},\cot \theta=-\frac{4}{\sqrt[]{65}},\sec \theta=\frac{9}{4},\csc \theta=-\frac{9}{\sqrt[]{65}}[/tex]what is the diameter of a circle if the circumference is 18 cm
PLEASE HURRY
What is the quotient of (−152) ÷ (−19) ÷ (−4)?
Answer:
-2
I did the math and it came out -2
Please show and explain this please
Answer:
b
Step-by-step explanation:
The root at [tex]x=1[/tex] has a multiplicity of 1, and corresponds to a factor of [tex](x-1)[/tex].
The root at [tex]x=-2[/tex] has a multiplicity of 1, and corresponds to a factor of [tex](x+2)[/tex].
The root at [tex]x=3[/tex] has a multiplicity of 2, and corresponds to a factor of [tex](x-3)^2[/tex].
ASAP I NEED HELP WITH THIS PROBLEM AND WILL GET THE BRAINLIEST FOR THE CORRECT ANSWER
Answer: (x, y) -> (x, -y)
Step-by-step explanation:
1) You can easily find the transformation by substituting one point on the figure.
For this example, I will substitute S and S' points. (4, 1) and (4, -1)
2) Replace the numbers with x and y.
Set the numbers equal. They are already equal so no change.
(4, 1) -> (4, -1)
Replace with X and Y
(x, y) -> (x, -y)
HELP NOW PLS !!! 100 POINTS
The points (5,8) and (10,2) fall on a particular line. What is its equation in point-slope form?
Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
Answer:
[tex]y-8=-\dfrac{6}{5}(x-5)[/tex]
Step-by-step explanation:
Define the given points:
(x₁, y₁) = (5, 8)(x₂, y₂) = (10, 2)First find the slope of the line by substituting the given points into the slope formula:
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{2-8}{10-5}=-\dfrac{6}{5}[/tex]
To find the equation in point-slope form, simply substitute the found slope and one of the given points into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-8=-\dfrac{6}{5}(x-5)[/tex]
Janet is getting balloons for her grandmother's birthday party. She wants each balloon string to be 12 feet long. At the party store, string is sold by the yard. If Janet wants to get 84 balloons, how many yards of string will she need?
Using conversion factors we can conclude that Janet needs 336 yards of string.
What do we mean by conversion factor?A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an equal value. For instance, 12 inches equals one foot when converting between inches and feet.So, yards of string are needed:
1 balloon string will be 12 feet longSo, 84 balloons will have:12 × 84 = 1,008 feet stringsWe know that:
1 feet = 0.3333 yardsThen, 1008 feet = 336 yardsTherefore, using conversion factors we can conclude that Janet needs 336 yards of string.
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I can't figure out how to do (i + j) x (i x j)for vector calc
In three dimensions, the cross product of two vectors is defined as shown below
[tex]\begin{gathered} \vec{A}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k} \\ \vec{B}=b_1\hat{i}+b_2\hat{j}+b_3\hat{k} \\ \Rightarrow\vec{A}\times\vec{B}=\det (\begin{bmatrix}{\hat{i}} & {\hat{j}} & {\hat{k}} \\ {a_1} & {a_2} & {a_3} \\ {b_1} & {b_2} & {b_3}\end{bmatrix}) \end{gathered}[/tex]Then, solving the determinant
[tex]\Rightarrow\vec{A}\times\vec{B}=(a_2b_3-b_2a_3)\hat{i}+(b_1a_3+a_1b_3)\hat{j}+(a_1b_2-b_1a_2)\hat{k}[/tex]In our case,
[tex]\begin{gathered} (\hat{i}+\hat{j})=1\hat{i}+1\hat{j}+0\hat{k} \\ \text{and} \\ (\hat{i}\times\hat{j})=(1,0,0)\times(0,1,0)=(0)\hat{i}+(0)\hat{j}+(1-0)\hat{k}=\hat{k} \\ \Rightarrow(\hat{i}\times\hat{j})=\hat{k} \end{gathered}[/tex]Where we used the formula for AxB to calculate ixj.
Finally,
[tex]\begin{gathered} (\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=(1,1,0)\times(0,0,1) \\ =(1\cdot1-0\cdot0)\hat{i}+(0\cdot0-1\cdot1)\hat{j}+(1\cdot0-0\cdot1)\hat{k} \\ \Rightarrow(\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=1\hat{i}-1\hat{j} \\ \Rightarrow(\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=\hat{i}-\hat{j} \end{gathered}[/tex]Thus, (i+j)x(ixj)=i-j
Let f(a) = x^2 + 5.a) Find the y-value when x = 0.The y-value, output value is ___b) Find the y-intercept, when x = 0.The y-intercept is ___c) Find the x-values, when y = 46.The x-values are ____
To solve a, we need to replace x = 0 in the formula of the function:
[tex]\begin{cases}f(x)=x^2+5 \\ x=0\end{cases}\Rightarrow f(0)=0^2+5=5[/tex]The y value when x = 0 is 5.
b is asking the same as a but in a different way. The y-intercept of a function is when x = 0, we just calculated that. The point of y-intercept is (0, 5)
Finally, to solve c, we need to find the values of x that gives us a value of f(x) = 46:
[tex]f(x)=46\Rightarrow46=x^2+5[/tex]Then solve:
[tex]\begin{gathered} x^2=46-5 \\ x=\pm\sqrt[]{41} \end{gathered}[/tex]Remember that we must that plus-minus the value when we take square root. ± √41 is the answer to c.
The prime factorization of $756$ is
\[756 = 2^2 \cdot 3^3 \cdot 7^1.\]Joelle multiplies $756$ by a positive integer so that the product is a perfect square. What is the smallest positive integer Joelle could have multiplied $756$ by?
The smallest positive integer Joelle could have multiplied 756 by
15876
This is further explained below.
What is a perfect square?Generally, A perfect square number is a number in mathematics that, when its square root is calculated, yields a natural number.
To solve this problem we can do:
[tex]\sqrt{756}[/tex]
By properties of roots
[tex]\begin{aligned}&\sqrt{756}=\sqrt{6\cdot126} \\&=\sqrt{6 * 6 * 21} \\\\ =\sqrt{6^2 * 21} \\&=6 \sqrt{21}\end{aligned}[/tex]
So, so that the multiplication of 756 by an integer becomes a perfect square, you have to multiply it by 21 to make $21^2$ and thus "eliminate" the root.
756 * 21=15876
In conclusion, You can verify that 15876is a perfect square since root (15876)=132 and 132 is a natural number
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The length of a rectangular room is 5 yards more than the width. If the area is 300 yd2, find the length and the width of the room.
Okay, here we have this:
Considering that the area of a rectangle is:
Area=length*width
Replacing we obtain:
300=(5+x)*x
300=5x+x²
0=5x+x²-300
0=(x-15)(x+20)
This mean that:
x-15=0 or x+20=0
x=15 or x=-20
And considering that the distances are positive we are left with the first solution, x=15; this mean that:
Width=15 yd
Length=(15+5) yd=20 yd.
Finally we obtain that the width is 15 yd and length is 20 yd.
The point (5,4) is rotated 270 degrees clockwise, would the answer be (-4,5)?
The image of the point (5, 4) after being rotated 270 degrees clockwise around the origin is (- 4, 5).
How to determine the image of a point by rotation around the origin
In this problem we find the case of a point to be rotated by a rigid transformation, represented by a rotation around the origin. The transformation rule is defined by the following expression:
P'(x, y) = (x · cos θ - y · sin θ, x · sin θ + y · cos θ)
Where:
(x, y) - Coordinates of point P(x, y).θ - Angle of rotation (counterclockwise rotation is represented by positive values).P'(x, y) - Coordinates of the resulting point.If we know that P(x, y) = (5, 4) and θ = - 270°, then the coordinates of the image are, respectively:
P'(x, y) = (5 · cos (- 270°) - 4 · sin (- 270°), 5 · sin (- 270°) + 4 · cos (- 270°))
P'(x, y) = (- 4, 5)
The image of the point (5, 4) is (- 4, 5).
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Jill works at a coffee shop on weekends. Every now and then, a customer will order a hot tea and ask Jill to surprise them with the flavor. The teas are categorized by flavor and caffeine level. Mint Fruity Caffeine-free 2 7 Caffeinated 5 5 What is the probability that a randomly selected tea is caffeinated or mint? Simplify any fractions.
The grand total is given by
[tex]n=2+7+5+5=19[/tex]so, the probability of Caffeinated is
[tex]P(Caffeinated)=\frac{5}{19}+\frac{5}{19}=\frac{10}{19}[/tex]the probability of mint is
[tex]P(\min t)=\frac{2}{19}+\frac{5}{19}=\frac{7}{19}[/tex]and the probability of the intersection is
[tex]P(Caffeinated\cap\min t)=\frac{5}{19}[/tex]Then, the probabilty of the union is given by
[tex]undefined[/tex]Answer choicesReflection:1. reflect in the x-axis2. No reflectionStretch/Compress:1. No stretch nor compression2. Vertical Stretch of 2Horizontal Translation:1. Shift 6 units left2. Shift 5 units left3. Shift 6 units right4. Shift 5 units rightVertical Translation:1. Shift 5 units up2. Shift 6 units down3. Shift 6 units up4. Shift 5 units down
First, the parent function is translated 5 units to the left, then it is reflected over the x-axis, and finally, it is translated 6 units down.
Answer:
Reflection: reflect in the x-axis.
Stretch: No stretch nor compression.
Horizontal Translation: Shift 5 units left.
Vertical Translation: Shift 6 units down.
An expert witness for a paternity lawsuit testifies that the length of a pregnancy is normally distributed with a mean of
280 days and a standard deviation of 13 days. An alleged father was out of the country from 242 to 301 days before the birth
of the child, so the pregnancy would have been less than 242 days or more than 301 days long if he was the father. The birth
was uncomplicated, and the child needed no medical intervention. What is the probability that he was NOT the father?
Calculate the z-scores first, and then use those to calculate the probability. (Round your answer to four decimal places.)
What is the probability that he could be the father? (Round your answer to four decimal places.)
1. The z scores in the question are - 2.92 and 1.615
2. The probability that he is the father = 0.054905
How to solve for the probability and the z scoreThe z score for the 242 days
= 242 - 280 / 13
= -2.92
The z score for the 30 days
= 301 - 280 / 13
= 1.615
Next we have to solve for The probability that he is not the father
this is written as
p(242 < x < 301)
p value of -2.92 = 0.00175
p value of 1.615 = 0.946845
Then we would have 0.946845 - 0.00175
= 0.945095
The probability that he is the father is given as 1 - probaility that he is not the father of the child
= 1 - .945095
= 0.054905
The probability that he is the father is 0.054905
What is probability?This is the term that is used in Statistics and also in the field of mathematics to explain the chances and the likelihood of an event occurring.
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