In the number 44,244, we can see two pairs of 4's.
The first pair (to the left) has a higher value than the second pair to the right, but the 4's have something in common: The leftmost 4 is ten times as high as the rightmost 4.
For this reason, we start the number as forty-four thousand and end up with forty-four.
Shaun deposits $3,000 into an account that has an rate of 2.9% compounded continuously. How much is in the account after 2 years and 9 months?
The formula for finding amount in an investment that involves compound interest is
[tex]A=Pe^{it}[/tex]Where
A is the future value
P is the present value
i is the interest rate
t is the time in years
e is a constant for natural value
From the question, it can be found that
[tex]\begin{gathered} P=\text{ \$3000} \\ i=2\frac{9}{12}years=2\frac{3}{4}years=2.75years \end{gathered}[/tex][tex]\begin{gathered} e=2.7183 \\ i=2.9\text{ \%=}\frac{2.9}{100}=0.029 \end{gathered}[/tex]Let us substitute all the given into the formula as below
[tex]A=3000\times e^{0.29\times2.75}[/tex][tex]\begin{gathered} A=3000\times2.21999586 \\ A=6659.987581 \end{gathered}[/tex]Hence, the amount in the account after 2 years and 9 months is $6659.99
The length of a rectangle is 2 inches more than its width.If P represents the perimeter of the rectangle, then its width is:oAB.O4Ос. РOD.P-2 별O E, PA
Given:
a.) The length of a rectangle is 2 inches more than its width.
Since the length of a rectangle is 2 inches more than its width, we can say that,
Width = W
Length = L = W + 2
Determine the width with respect to its Perimeter, we get:
[tex]\text{ Perimeter = P}[/tex][tex]\text{ P = 2W + 2L}[/tex][tex]\text{ P = 2W + 2(W + 2)}[/tex][tex]\text{ P = 2W + 2W + }4[/tex][tex]\text{ P = 4W + }4[/tex][tex]\text{ P - 4 = 4W}[/tex][tex]\text{ }\frac{\text{P - 4}}{4}\text{ = }\frac{\text{4W}}{4}[/tex][tex]\text{ }\frac{\text{P - 4}}{4}\text{ = W}[/tex]Therefore, the answer is D.
If two lines intersect to form a right angle, then they are
..(perpendicular, parallel, obtuse
A store is having a " 15 % off sale on perfume . You have a coupon for 50 % off any perfume . What is the final price , in dollars , of a $ 30 bottle of perfume ? If necessary round your answer to the nearest cent .
ANSWER
$12.75
EXPLANATION
The store is selling the perfumes at 15% off the original price, so if a bottle of perfume costs $30, then they are selling it at,
[tex]30\cdot\frac{100-15}{100}=30\cdot\frac{85}{100}=30\cdot0.85=25.50[/tex]But you also have a coupon for 50% off, so you get to buy the perfume at half that price,
[tex]25.50\cdot\frac{50}{100}=25.50\cdot0.5=12.75[/tex]Hence, the final price of the perfume is $12.75.
A person standing 306 feet from the base of a church observed the angle of elevation to the church’s steeple to be 20°. How tall is the church. Give answer to the nearest whole number
Solution
- The solution steps are given below:
[tex]\begin{gathered} \text{ Applying SOHCAHTOA, we have:} \\ \frac{h}{306}=\tan20 \\ h=306\tan20 \\ \\ h=111.374...ft\approx111ft\text{ \lparen To the nearest whole number\rparen} \end{gathered}[/tex]Final Answer
111 ft
the mean monthly water bill for 82 residents in a local apartment complex is 137 dollars. what is the best point estimate for the mean monthly water bill for all residents of the local apartmemt complex?
From the information given, the mean monthly water bill for 82 residents in a local apartment complex is 137 dollars. The best estimate for the mean monthly water bill is the sample mean. Since 137 dollars is the sample mean, the correct answer is 137
please help me solve this no tutor can ahelp me
Solution:
Since the confidence interval width is inversely proportional to n , the answer is the smallest n.
CORRECT OPTION: 36
Teachers' Salaries The average annual salary for all U.S. teachers is $47,750. Assume that the distribution is normal and the standard deviation is $5680Find the probabilities.P (X>45,500)
there are 3 members on a hockey team (including all goalie) at the end of a hockey game each member if the team shakes hands with each member of the opposing team. how many handshakes occur?
-6 subtracted from a number equals -12.What is the number?
Answer:
The number is -18
Explanation:
-6 subtracted from a number equals -12.
We want to find the value of the number
Let the number be x
We can write the statement mathematically as:
[tex]x-(-6)=-12[/tex]Solving this equation, the value of x is the number we are required to find.
[tex]\begin{gathered} x+6=-12 \\ \text{Subtract 6 from both sides} \\ x+6-6=-12-6 \\ x=-18 \end{gathered}[/tex]The said number is -18
I have 4 questions I need help with This is first question number 2
We have the next function that models the Australian GDP since 1960 :
[tex]G(i)=1806x(1.037)^t[/tex]Where t is the number of years since 1960.
a)If we are in the year 1960, it means t=0
Therefore:
[tex]G(t)=1806x(1.037)^1[/tex][tex]G(0)=1806x(1.037)^0[/tex][tex]G(0)=1806[/tex]b)Now, we need to find the Australia capita in 1963.
This means t=3
Therefore:
[tex]G(t)=1806x(1.037)^t[/tex][tex]G(3)=1806x(1.037)^3[/tex][tex]G(3)=2013.974721[/tex]c) We need to find when the function is equal to 100,000.
Therefore we equal the function G(t)=100,000.
Then:
[tex]1806x(1.037)^t=1000000[/tex]Solve for t:
Divide both sides by 1806:
[tex]\frac{1806x(1.037)^t}{1806}=\frac{100000}{1806}[/tex][tex](1.037)^t=\frac{50000}{903}[/tex]Add Ln for each side:
[tex]\ln (1.037)^t=in(\frac{50000}{903})[/tex][tex]t\ln (1.037)=in(\frac{50000}{903})[/tex]Then:
[tex]t=\frac{in(\frac{50000}{903})}{\ln (1.037)}[/tex][tex]t=110.48286[/tex]Rounded to the nearest year:
[tex]t=110[/tex]Therefore: 1960 +110 = 2070
On 2070 the Austranlian GDP reaches 100,000 USD
if you copy a page on a machine at 60%, you should get a similar copy of the page. What is the corresponding setting to obtain the original from the copy? The corresponding setting to obtain the original from the copy is _______%
Answer:
The corresponding setting to obtain the original from the copy is 166.67%
[tex]166\frac{2}{3}\text{\%}[/tex]Explanation:
Let c and x represent the copy and original respectively;
[tex]c=60\text{\% of x}[/tex]making x the subject of formula;
[tex]\begin{gathered} c=0.6x \\ x=\frac{c}{0.6} \\ x=1\frac{2}{3}c \\ in\text{ percentage;} \\ x=1\frac{2}{3}c\times100\text{\%} \\ x=166.67\text{\% of c} \end{gathered}[/tex]Therefore, The corresponding setting to obtain the original from the copy is 166.67%
[tex]166\frac{2}{3}\text{\%}[/tex]Rewrite the polynomial expression using the GCF: 4x^2+8x+24 ?What is the new polynomial expression
GCF of 4,8 and 24
is. = 4
Then new expression is
y = 4• (x^2 + 2x + 6)
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Write the equation for a parabola with a focus at (-6,0) and a directrix at x = -2.
x=
y² = -8(x - 4), which is the required equation of the parabola.
What are a parabola's focus and directrix ?All points in a plane that are equally spaced out from a given point and a given line make up a parabola.
The line is known as the directrix, and the point is known as the parabola's focus.
A parabola's axis of symmetry is perpendicular to the directrix, which does not touch the parabola.
The focus of the parabola is F(-6,0) and its directrix is the line x=−2 i.e., x+2=0
Let P(x,y) be any point in the plane of directrix and focus, and MP be the perpendicular distance from P to the directrix,then P lies on parabola if FP=MP
⇒(x+6)²+(y−0)² = ∣x+2∣÷1
⇒x² + 12x+36+y² = x² +4x +4
⇒y² + 8x = -32
⇒y² = - 8x - 32
⇒y² = -8(x - 4)
⇒ y² = -8(x - 4), which is the required equation of the parabola.
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The circle graph shows how the annual budget for a company is divided by department. If the amount budgeted for support, sales, and media combined is $25,000,000, what is the total annual budget?
Answer: $50,000,000
Explanation:
First, we add up the percentage of support, sales, and media covers. Given that:
Support = 23%
Sales = 22%
Media = 5%
The total percentage would be
[tex]23\%+22\%+5\%=50\%[/tex]This would mean that $25,000,000 covers half of the annual budget. The other half would be of the same amount, therefore, the total annual budget would be:
[tex]\begin{gathered} 50\%+50\%=100\% \\ \$25,000,000+\$25,000,000=\$50,000,000 \end{gathered}[/tex]Consider the following equation find the X- and y- Intercepts, if possible
Answer:
x-intercept: (-1/2, 0)
y-intercept: (0, 1)
Explanation:
The x-intercept is the point where the graph crosses the x-axis, so to find the x-intercept, we need to replace y = 0 on the given equation and solve for x
y - 2x = 1
0 - 2x = 1
-2x = 1
-2x/(-2) = 1/(-2)
x = -1/2
Then, the x-intercept is (-1/2, 0)
The y-intercept can be calculated replacing x = 0 and solving for y, so
y - 2x = 1
y - 2(0) = 1
y - 0 = 1
y = 1
Then, the y-intercept is (0, 1)
Therefore, the answers are
x-intercept: (-1/2, 0)
y-intercept: (0, 1)
Can't help me??
x/4 - 9 = 7
solve the equation... use transposing method
The Answer Is x = 64.
Explanation.x/4 - 9 = 7
x/4 = 7 + 9
x/4 = 16
x = 16 × 4
x = 64
_________________
Class: High School
Lesson: Equation
[tex]\boxed{ \colorbox{lightblue}{ \sf{ \color{blue}{ Answer By\:Cyberpresents}}}}[/tex]
Answer:
x = 64
Step-by-step explanation:
x/4 - 9 =7
Step 1: Add 9 to both sides
x/4 - 9 + 9 = 7 + 9
x/4 = 16
Step 2: Multiply right side by 4
x/4= 16 x 4
x = 64
Step 3: Prove your x-value
64/4 = 16 - 9 = 7
64/4 - 9 = 7
So x = 64
PS: Please make brainliest.
Write equation for graph ?
The equation for parabolic graphed function is y = [tex]-3x^{2} -24x-45[/tex].
What is parabola graph?
Parabola graph depicts a U-shaped curve drawn for a quadratic function. In Mathematics, a parabola is one of the conic sections, which is formed by the intersection of a right circular cone by a plane surface. It is a symmetrical plane U-shaped curve. A parabola graph whose equation is in the form of f(x) = ax2+bx+c is the standard form of a parabola.
The given graph has 2 intercept at x axis x = -3, x = -5
y = a (x+3) (x+5)
using the intercept (-4, 3)
3 = a (-4 +3)(-4+5)
3 = a (-1)(1)
a =-3
y = -3(x+3)(x+5)
y = -3 [x(x+5) +3(x+5)]
y = [tex]-3x^{2}-24x-45[/tex]
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The data shows the total number of employee medical leave days taken for on-the-job accidents in the first six months of the year: 12, 6, 15, 9, 28, 12. Use the data for the exercise. Find the standard deviation.
ANSWER:
The standard deviation is 7
STEP-BY-STEP EXPLANATION:
The standard deviation formula is as follows
[tex]\sigma=\sqrt[]{\frac{\sum^N_i(x_i-\mu)^2_{}}{N}}[/tex]The first thing is to calculate the average of the sample like this:
[tex]\begin{gathered} \mu=\frac{12+6+15+9+28+12}{6} \\ \mu=\frac{82}{6}=13.67 \end{gathered}[/tex]Replacing and calculate the standard deviation:
[tex]\begin{gathered} \sigma=\sqrt[]{\frac{(12_{}-13.67)^2_{}+(6_{}-13.67)^2_{}+(15_{}-13.67)^2_{}+(9_{}-13.67)^2_{}+(28-13.67)^2_{}+(12_{}-13.67)^2_{}}{6}} \\ \sigma=\sqrt[]{\frac{293.33}{6}} \\ \sigma=6.99\cong7 \end{gathered}[/tex]anumeha mows lawns she charges an initial fee and constant fee for each hour of work
Given the function:
[tex]F(t)=6+12t[/tex]Where F represents Anumeha's fees (in dollars) for working t hours. The initial fee can be calculated for t = 0:
[tex]F(0)=6+12\cdot0=6[/tex]So the constant fee is $6. Now, we need to calculate how much does she charges each hour. We can calculate the values at t = 1, t = 2, and t = 3:
[tex]\begin{gathered} F(1)=6+12\cdot1=18 \\ F(2)=6+12\cdot2=30 \\ F(3)=6+12\cdot3=42 \end{gathered}[/tex]As we can see, there is a constant increment of $12 for each hour. Then, Anumeha charges $12 for each hour of work.
1) Circle the tables that represent y as a function of x.хХ-31X-10у-5515-3y3608-2-4- 1-2-2-5- 1290у-1-1- 1-11-2-52-5
The answer is the last table
The answer is the last table
Open the image attached belowProve that:sec n/(tan n + cot n) = sin n
Given:
We are required to prove:
[tex]\frac{\sec\text{ }\theta\text{ }}{\tan\text{ }\theta\text{ + cot}\theta}\text{ = sin}\theta[/tex]From the left-hand side:
[tex]\begin{gathered} =\frac{\sec\text{ }\theta\text{ }}{\tan\text{ }\theta\text{ + cot}\theta}\text{ } \\ =\text{ }\frac{\frac{1}{\cos\theta}}{\frac{\sin\theta}{\cos\theta}\text{ + }\frac{\cos \theta}{\sin \theta}} \\ =\text{ }\frac{\frac{1}{\cos\theta}}{\frac{\sin ^2\theta+cos^2\theta}{\sin \theta\cos \theta}} \\ \end{gathered}[/tex]From standard trigonometric identity, we have:
[tex]\sin ^2\theta+cos^2\theta\text{ = 1}[/tex]Substituting we have:
[tex]\begin{gathered} =\text{ }\frac{\frac{1}{\cos\theta}}{\frac{1}{\sin \theta\cos \theta}} \\ =\text{ }\frac{\sin \theta\cos \theta}{\cos \theta} \\ =\text{ sin }\theta\text{ (Right-hand side)} \end{gathered}[/tex]What is the equation, in slope-intercept form, of a line that passes through the points(-8,5) and (6,5)?
Given the points (-8,5) and (6,5), we can find the equation of the line first by finding the slope with the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]in this case, we have the following:
[tex]\begin{gathered} (x_1,y_1)=(-8,5) \\ (x_2,y_2)=(6,5) \\ \Rightarrow m=\frac{5-5}{6-(-8)}=\frac{0}{6+8}=0 \\ m=0 \end{gathered}[/tex]since the slope is m = 0, we have that the line is a horizontal line that goes through the points (-8,5) and (6,6), then, the equation of the line is:
[tex]y=5[/tex]in slope-intercept form the equation would be:
[tex]y=0x+5[/tex]Need to graph and then mark length of stay (in days) on the bottom of the graph. Need 4 points on graph and 4 number on bottom of graph
given the data
13,9,5,11,6,3,12,10,11,7,3,2,2,2,10,10,12,12,12,8,8
sort data
s= 2, 2, 2, 3, 3, 5, 6, 7, 8, 8, 9, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13
then we have
2 ---- 3
3 ----- 2
5----- 1
6 ---- 1
7 -----1
8------2
9 ------1
10-----3
11-------2
12------4
13-------1
The volume of cylinder is 504 pi cm^(3) & height is 14cm Find the curved surface area 8 total surface area.
The Solution:
The correct answers are:
Curved surface area = 527.79 squared centimeters
Total surface area = 753.98 squared centimeters.
Given that the volume of a cylinder with height 14cm is
[tex]504\pi cm^3[/tex]We are required to find the curved surface area and the total surface area of the cylinder.
Step 1:
We shall find the radius (r) of the cylinder by using the formula below:
[tex]V=\pi r^2h[/tex]In this case,
[tex]\begin{gathered} V=\text{volume =504}\pi cm^3 \\ r=\text{ radius=?} \\ h=\text{ height =14cm} \end{gathered}[/tex]Substituting these values in the above formula, we get
[tex]504\pi=\pi r^2\times14[/tex]Finding the value of r by first dividing both sides, we get
[tex]\begin{gathered} \frac{504\pi}{14\pi}=r^2 \\ \\ r^2=36 \end{gathered}[/tex]Taking the square root of both sides, we get
[tex]\begin{gathered} \sqrt[]{r^2}\text{ =}\sqrt[]{36} \\ \\ r=6\operatorname{cm} \end{gathered}[/tex]Step 2:
We shall find the curved surface area by using the formula below:
[tex]\text{CSA}=2\pi rh[/tex]Where
[tex]\begin{gathered} \text{ CSA=curved surface area=?} \\ h=14\operatorname{cm} \\ r=6\operatorname{cm} \end{gathered}[/tex]Substituting these values in the formula above, we have
[tex]\text{CSA}=2\times6\times14\times\pi=168\pi=527.788\approx527.79cm^2[/tex]Step 3:
We shall find the total surface area by using the formula below:
[tex]\text{TSA}=\pi r^2+\pi r^2+2\pi rh=2\pi r^2+2\pi rh[/tex]Where
TSA= total surface area and all other parameters are as defined earlier on.
Substituting in the formula, we get
[tex]\text{TSA}=(2\pi\times6^2)+(2\pi\times6\times14)=72\pi+168\pi[/tex][tex]\text{TSA}=240\pi=753.982\approx753.98cm^2[/tex]Therefore, the correct answers are:
Curved surface area = 527.79 squared centimeters
Total surface area = 753.98 squared centimeters.
The directions for a weed spray concentrate state that 3 tablespoons of the concentrate should be mixed with 4 gallons of water. How many tablespoons of concentrate need to be mixed with 5 gallons of water?
The given information is:
- 3 tablespoons of the concentrate should be mixed with 4 gallons of water.
The ratio of tablespoons to gallons of water is:
[tex]\frac{3\text{ tablespoons}}{4\text{ gallons of water}}[/tex]Then, we can apply proportions to find how many tablespoons of concentrate need to be mixed with 5 gallons of water, so:
[tex]\begin{gathered} \frac{3}{4}=\frac{x}{5} \\ Isolate\text{ x} \\ x=\frac{5*3}{4} \\ x=\frac{15}{4} \\ x=3.75\text{ tablespoons} \end{gathered}[/tex]It is needed 3.75 tablespoons of the concentrate.
What is the answer to this equation?
Answer:
D 7.5
Step-by-step explanation:
n + n-3 + 2n-4 = perimeter ≥ 37
4n-7≥37
4n≥30
n≥7.5
The first part of the function rule for the values in the table below is Y equals X over two. What is the complete function rule?
Given:
The tabular representation having different values of x and y.
Required:
The relation between x and y.
Explanation:
When x = 6 and y = 2,
[tex]y\text{ = }\frac{6}{2}\text{ = 3 }\Rightarrow\text{ 3 - 1 = 2 = x}[/tex]When x = 8 and y = 3,
[tex]y\text{ = }\frac{8}{2}\text{ = 4 }\Rightarrow\text{ 4-1 = 3}[/tex]When x = 10 and y = 4,
[tex]undefined[/tex]bridget is growing seven plants for her science project. here are the heights of the plants after four weeks. what is the mode?
Given the data:
Plant Height(Cm)
1 9
2 10
3 10
4 6
5 9
6 7
7 10
The mode of a data set is the value that occurs most frequently.
From the data above, the height that occurs most frequently is 10 cm.
Therefore, the mode is 10.
ANSWER:
Which equation could be represented by the number line? O A. -5 + 7 = 2 O.B. -3+(-4)= -7 O C. 4+ (-7)=-3 O D.7+(-6) = 1 SURAT E PREVIOUS
C. 4 + (-7) = -3
C. 4 + (-7) = -3 could represent by the number line because no other equation has reflected the lines' displacement of 7 grid from a certain point going to the left which is equivalent to -7.
The rest of the choices is not a possible equation to the line.
A. -5 + 7 = Displacement of 7 Grid to the Right from Point -5
B. -3 - 4 = Displacement of 4 Grid to the Left from Point -3
D. 7 - 6 = Displacement of 6 Grid to the Left from Point 7
