Let's begin by identifying key information given to us:
Number of times she woke early (e) = 6
Total number of days (t) = 80 days
The percentage of days she's been getting up early is given by:
[tex]\begin{gathered} \text{\%}n\text{=}\frac{e}{t}\cdot100\text{\%} \\ \text{\%}n=\frac{6}{80}\cdot100\text{\%} \\ \text{\%}n=7.5\text{\%} \end{gathered}[/tex]Mary has gotten up early 7.5% of the days
1) Triangle FGI has vertices F (3, 1). G (1. 5) and I (6. 4) What are the coordinates of the point of the orthocenter?
We have to find the orthocenter of the triangle FGI.
We start by graphing the vertices F, G and I:
The next step is to calculate the slope of each segment, then its perpendicular line that pass through the other vertex of the triangle (not included in the segment).
With two segments is enough to calculate the orthocenter.
Segment GI.
Slope:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{5-4}{1-6}=\frac{1}{-5}=-\frac{1}{5}[/tex]Perpendicular slope:
[tex]m_p=-\frac{1}{m}=-\frac{1}{-\frac{1}{5}}=5[/tex]Line equation (perpendicular) that pass through F(3,1):
[tex]\begin{gathered} y-1=5\cdot(x-3) \\ y=5x-15+1 \\ y=5x-14 \end{gathered}[/tex]Segment GF.
Slope:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{5-1}{1-3}=\frac{4}{-2}=-2[/tex]Perpendicular slope:
[tex]m_p=-\frac{1}{m}=-\frac{1}{-2}=\frac{1}{2}[/tex]Line equation (perpendicular) that pass through I(6,4):
[tex]\begin{gathered} (y-4)=\frac{1}{2}(x-6) \\ y=\frac{1}{2}x-3+4 \\ y=\frac{1}{2}x+1 \end{gathered}[/tex]Then, with two lines, we can find the intersection:
[tex]\begin{gathered} y=\frac{1}{2}x+1=5x-14 \\ \frac{1}{2}x-5x=-14-1 \\ \frac{1}{2}x-\frac{10}{2}x=-15 \\ -\frac{9}{2}x=-15 \\ x=-15\cdot-\frac{2}{9}=\frac{30}{9}=\frac{10}{3}\approx3.33 \\ y=5\cdot x-14=5\cdot\frac{10}{3}-14=\frac{50}{3}-\frac{42}{3}=\frac{8}{3}\approx2.67 \end{gathered}[/tex]The orthocenter is (x,y) = (10/3, 8/3) = (3.33, 2.67)
PLEASE HELP I NEED THIS DONE BEFORE TOMORROW A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm. after d days f(d) = 11(1.01)^d Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm. What is a reasonable domain to plot the growth function points) Part B: What does the y-intercept of the graph of the function f(d) represent? (2 points) Part C: What is the average rate of change of the function f(d) from d = 2 to d=7 and what does it represent (4 points)
The radius is given to be;
[tex]f(d)=11(1.01)^d[/tex]Part A
To find the domain
First plud d =0
[tex]f(0)=11(1.01)^0=11\times1=11[/tex]Next plug in f(d) = 11.79 into the radius diven and solve for d
That is;
[tex]11.79=11(1.01)^d[/tex]Divide both-side by 11
[tex]\frac{11.79}{11}=(1.01)^d[/tex][tex]1.07181818=1.01^d[/tex]Take the log of both-side
[tex]\log 1.07181818=d\log 1.01[/tex][tex]d=\frac{\log 1.07181818}{\log 1.01}[/tex][tex]d=6.97[/tex]The domains are;
(11, 0) and (11.79, 6.97)
Part B
The y-intercept is when d =0, this gives a radius of 11 and it represent
the initial radius. That is, the radius of the algae before starting the study.
Part C
First let's find the values of f(d) when d = 2 and 7 respectively
for d=2
substitute d=2 in the equation of the radius given
[tex]f(2)=11(1.01)^2=11(1.0201)=11.2211[/tex]when d=7
substitute d = 7 in the equation of the radius given
[tex]f(7)=11(1.01)^7=11(1.072136)=\text{ 11.7935}[/tex][tex]\text{Rate of change =}\frac{f(7)-f(2)}{7-2}[/tex][tex]=\frac{11.7935-11.2211}{7-2}[/tex][tex]=\frac{0.5724}{5}[/tex][tex]=0.11448[/tex]The rate of change is 0.11448 and it represent the slope of the graph from d=2 to d=7
Find f(–2), if f(x) = −3x^2 – 5x + 11
To solve the exercise, replace x = -2 in the function and operate, like this
[tex]\begin{gathered} f\mleft(x\mright)=-3x^2-5x+11 \\ f(-2)=-3(-2)^2-5(-2)+11 \\ f(-2)=-3\cdot4+10+11 \\ f(-2)=-12+10+11 \\ f(-2)=9 \end{gathered}[/tex]Therefore, the value of the function is 9 when x = -2.
What theorem needs to be used before showing the triangles are congruent? What theorem proves these triangles are congruent?
Given AD║CB
AE = CE
AED ≈CEB
Side Angle Side
Side AE
Side and Angle are equal to CE same angle same side.
Using that we can prove all angles are in fact congruent.
First three boxes are Side Angle Side
you were given a rectangle with dimension of length equals 60 inches and width equals 4J the perimeter of the rectangle is 400 in what is the value of j
Given data:
The given length of the rectangle is L=60 inches.
The given width of the rectangle is bB=4J.
The perimeter of the rectangle is P=400 inches.
The expression for the perimeter of the rectangle is,
P=2(L+B)
Substitute the given values in the above expression.
400 inches=2(60 inches+4J)
200 inches=60 inches+4J
140 inches=4J
J=35 inches
Thus, the value of J is 35 inches.
how many springs solutions exist for the following system of equations? y=-3x+2y=2x
To find the solutions, first, we make the equations equal as follows
[tex]\begin{gathered} y=y \\ -3x+2=2x \end{gathered}[/tex]Then, we solve for x
[tex]\begin{gathered} 2=2x+3x \\ 2=5x \\ x=\frac{2}{5} \end{gathered}[/tex]Then, we find y
[tex]\begin{gathered} y=2x \\ y=2\cdot\frac{2}{5}=\frac{4}{5} \end{gathered}[/tex]Hence, the solution to the system is (2/5, 4/5).Adrian Ahren invests ₱350,000 at 16% interest compounded quarterly, for 7 years. Find thecompound amount of Adrian Ahren’s investment.
Compound amount is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex][tex]\begin{gathered} A=\text{ final amount} \\ P=\text{ Initial amount} \\ r=\text{ interest rate} \\ n=\text{ number of times interest applied per time period} \\ t=\text{ number of time periods} \end{gathered}[/tex]Initial amount (p) = 350000.
Time (t) = 7
n = 4 (quarterly)
r (interest rate) = 16%
[tex]\begin{gathered} r=\frac{16}{100} \\ r=0.16 \end{gathered}[/tex][tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=350000(1+\frac{0.16}{4})^{4\times7} \\ A=350000(1+0.04)^{28} \\ A=350000\times2.998 \\ A=1049546.16 \end{gathered}[/tex]Find the intercepts of the function.g(n) = −3(3n − 1)(4n + 1)n-intercept (n, g(n)) = (smaller n-value)n-intercept (n, g(n)) = (larger n-value)y-intercept (n, g(n)) =
In order to find the n-intercepts of the function, let's equate each factor to zero:
[tex]\begin{gathered} -3(3n-1)(4n+1)=0\\ \\ \begin{cases}3n-1=0\rightarrow n=\frac{1}{3}{} \\ 4n+1=0\rightarrow n=-\frac{1}{4}{}\end{cases} \end{gathered}[/tex]So the n-intercept with the smaller n-value is (-1/4, 0) and the n-intercept with the larger n-value is (1/3, 0).
Now, to find the y-intercept, let's use n = 0 and calculate the value of g(n):
[tex]\begin{gathered} g(n)=-3(3n-1)(4n+1)\\ \\ g(0)=-3(3\cdot0-1)(4\cdot0+1)\\ \\ g(0)=-3(-1)(1)\\ \\ g(0)=3 \end{gathered}[/tex]Therefore the y-intercept is (0, 3).
RST stock has an annual dividend per share of $4.35 and a closing price per share of 39.50. What is the yield % for RST stock (to the nearest tenth of a percent)? Note: Yield% = (annual dividend per share) + (closing price per share).8.7%9.9%11.0%12.2%None of these choices are correct.
Step 1
Yield% = (annual dividend per share) / (closing price per share)
[tex]\begin{gathered} Yield\text{ \%}=\frac{\text{annual dividend per share}}{\text{closing price per share}} \\ \\ Yield\text{ \%}=\frac{4.35}{39.50} \\ \\ Yield\text{ \%}=\text{ 0.11} \end{gathered}[/tex]15A somewhat outdated study indicates that the mean number of hours worked per week by software developers is 44. We have good reason to suspect that the mean number of hours worked per week by software developers, μ, is now greater than 44 and wish to do a statistical test. We select a random sample of software developers and find that the mean of the sample is 48 hours and that the standard deviation is 4 hours.Based on this information, complete the parts below.(a)What are the null hypothesis H0 and the alternative hypothesis H1 that should be used for the test?H0:H1:(b)Suppose that we decide to reject the null hypothesis. What sort of error might we be making?type 1 or type 2?(c) Suppose the true mean number of hours worked by software engineers is 50 hours. Fill in the blanks to describe a Type II error.A Type II error would be ______ the hypothesis that μ is ______, ______ when, in fact, μ is ______.
Part A:
The null hypothesis is the commonly accepted fact. It is the opposite of the alternative hypothesis for which the researchers have a good reason to suspect.
The null and alternative hypothesis are the following:
H₀: μ = 44 (Since it is established that the mean number of hours per week is 44)
H₁: μ > 44 (Since the researchers suspect that it is greater than 44)
Part B:
This table simplifies the type of errors that could be committed when rejecting or accepting the null hypothesis.
Should we reject the null hypothesis, but it turns out to be true. Then the error that we have committed is Type I.
Part C:
A Type II error happens when we fail to reject the null hypothesis when in fact the alternative hypothesis is true.
Suppose that the true mean number of hours worked by software engineers is 50 hours, then a type II error would be failing to reject the hypothesis that μ is equal to 44, when in fact μ is greater than 44.
Consider 0.3 x 0.1.How many digits after the decimal point will the product have?Numbers of digits =
In this case the number of digits after the decimal pointmust be 2 because each number has one digit after the decimal point.
express as a single power: -(8)^5 x (-8)^10
Answer:
[tex]-8^{15}[/tex]Step-by-step explanation:
Using the product of powers rules, which is represented as:
[tex]a^m*a^n=a^{m+n}[/tex]Therefore, for the given expression:
[tex]-8^5*-8^{10}=-8^{5+10}=-8^{15}[/tex]Do you know what 6.756 x 108.62 is?
Evaluate the produt of decimal number 6.756 and 108.62.
[tex]\begin{gathered} 6.756\times108.62=\frac{6756}{1000}\times\frac{10862}{100} \\ =\frac{6756\cdot10862}{1000\cdot100} \\ =\frac{73383672}{100000} \\ =733.83672 \end{gathered}[/tex]So answer is 733.83672.
3/5 greater or least 7/10. I need to use compare fractions common numerator
We have the following fractions
[tex]\frac{3}{5}\text{ and }\frac{7}{10}[/tex]We know that if the denominators of two fractions are the same then the fraction with the largest numerator is the larger fraction.
Then, we need to convert the denominator of one fraction so they both have the same denominator. For instance, if we multiply and divide by 2 the first fraction, we have an equivalent fraction, that is,
[tex]\frac{3}{5}=\frac{3}{5}\times\frac{2}{2}=\frac{6}{10}[/tex]This means that 3/5 is equivalent to 6/10 but in the last form 6/10 and 7/10 have the same denominator, so we can compare their numerators. In other words, we need to compare
[tex]\frac{6}{10}\text{ and }\frac{7}{10}[/tex]Since 7 is greater than 6 then:
[tex]\frac{3}{5}<\frac{7}{10}[/tex]Instead of converting 3/5, we can convert the fraction 7/10. If we multiply and divide 7/10 by 1/2, we have
[tex]\frac{7}{10}=\frac{\frac{7}{2}}{\frac{10}{2}}=\frac{3.5}{5}[/tex]Now, we can compare these fractions:
[tex]\begin{gathered} \frac{3}{5}\text{ and }\frac{3.5}{5} \\ \sin ce\text{ 3.5 is greater that 3, then} \\ \frac{3}{5}<\frac{7}{10} \end{gathered}[/tex]Is there a proportional relationship between x and y? Explain. if you would like the options let me know!!
A proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if:
y=kx
for some constant k , called the constant of proportionality .This means that as x increases, y increases and as x decreases, y decreases-and that the ratio between them always stays the same.
Here, as the ratios x/y and y/x are not folowed, through all the sets of x and y, it is not a proportional relationship.
Thus, first option is correct
ashely was born on 12/22/2001. how many eight-digit codes could she make using digits in her birthday?
We have 8 digits:
[tex]1,2,2,2,2,0,0,1[/tex]So, the number of combinations is:
[tex]C=8!=40320[/tex]However:
2 is repeated 4 times
0 is repeated 2 times
1 is repeated 2 times
Therefore:
[tex]T=\frac{40320}{4!\cdot2!\cdot2!}=420[/tex]Answer:
420
at the end of the holiday season in January, the sales at a department store are expected to fall. It was initially estimated that for the x day of January, The sales will be s(x). The financial analysis at the store correct other projection and are not expecting the total sales for the X day of January to be t(x)T(1)=
Use trigonometric identities, algebraic methods, and inverse trigonometric functions, as necessary, to solve the following trigonometric equation on the interval [0, 21).Round your answer to four decimal places, if necessary. If there is no solution, indicate "No Solution."3sin?(x) + 13sin(x) = -12
Answer:
No solution
Explanation:
The equation
[tex]3(\sin x)^2+13\sin x=-12[/tex]looks very much like a quadratic equation. Therefore, for the moment we say that
[tex]y=\sin x[/tex]and write the above equation as
[tex]\begin{gathered} 3y^2+13y=-12 \\ \Rightarrow3y^2+13y+12=0 \end{gathered}[/tex]Using the quadratic formula, we find that the solutions to the above equation are given by
[tex]y=\frac{-13\pm\sqrt[]{13^2-4(3)(12)}}{2\cdot3}[/tex][tex]\begin{gathered} y=-\frac{4}{3} \\ y=-3 \end{gathered}[/tex]Reminding ourselves that actually y was sin(x) gives
[tex]undefined[/tex]Find dy/dx of y^2-2xy=16
Question 4 What is the z score in the following data set, for the value of x = 14? Consider this data set to represent the entire population. Round to two decimal places, if necessary. 6, 12, 9, 8, 15, 5, 7, 10, 11, 13 n't know One attempt 1.45 1.42 1.43 You answered 3 out of 3 correctly. Asking up to 7
The value of the z-score for the value x = 14 is 1.45
To get the z-score, we need the value of the mean and the standard deviation
We can get the mean by adding up all the numbers and dividing by the count of values
We have this as follows;
[tex]\begin{gathered} \frac{6+12+9+8+15+5+7+10+11+13}{10} \\ =\text{ }\frac{96}{10}\text{ = 9.6} \end{gathered}[/tex]We also need the value of the standard deviation
We have the value of this as 3.04
The formula for the z-score is;
[tex]\frac{x-\operatorname{mean}}{SD}[/tex]x in this case is the value 14
So, we have that;
[tex]\frac{14-9.6}{3.04}\text{ =1.45}[/tex]Yasin performs the elementary row operation represented by R2 - ½ R1 on matrix A.
We are given a matrix of
[tex]\begin{bmatrix}{4} & {3} & {0} \\ {-6} & {-3} & {12} \\ {} & {} & \end{bmatrix}[/tex]Yasin performs R2 - 1/2R1
The second row and column will be
For the first row
-6 - 1/2(4)
-6 - 2
= -8
For the second row
-3 - 1/2(3)
= -3 -3/2
= -2 * 3 / 1 - 3 x 2 / 2 / 2
= -6 - 3 / 2
= -9/2
Third row
12 - 1/2(0)
= 12 - 0
12
The new matrix is
[tex]\begin{bmatrix}{4} & {3} & {0} \\ {-8} & {-\frac{9}{2}} & {12} \\ {} & {} & {}\end{bmatrix}[/tex]find width of w in a V-slot 48° angle of the V, 8.4cm height?
Notice that we can draw a line that bisects the angle A to get the following right triangle:
we can find the length of w' using the function tangent:
[tex]\begin{gathered} \tan (24)=\frac{\text{opposite side}}{adjacent\text{ side}}=\frac{w^{\prime}}{8.4} \\ \Rightarrow w=8.4\cdot\tan (24)=3.74 \\ w^{\prime}=3.74 \end{gathered}[/tex]since w' is only the half of w, we have that w is:
[tex]w=2\cdot w^{\prime}=2(3.74)=7.48_{}[/tex]therefore, w = 7.48
An old dot-matrix printer took 11 minutes to print 2.5 pages. If 12 pages are going to be printed, how many minutes should this take?
We can use the following rate to solve the exercise.
[tex]\frac{11\text{ minutes}}{2.5\text{ pages}}=\frac{x}{12\text{ pages}}[/tex]Now, we solve for x:
[tex]\begin{gathered} \text{ Multiply by 12 pages from both sides} \\ \frac{11\text{ minutes}}{2.5\text{ pages}}\cdot12\text{ pages}=\frac{x}{12\text{ pages}}\cdot12\text{ pages} \\ \frac{11\text{ minutes }\cdot12\text{ pages}}{2.5\text{ pages}}=x \\ \frac{11\cdot12}{2.5}\text{ minutes}=x \\ \frac{132}{2.5}\text{ minutes}=x \\ 52.8\text{ minutes }=x \end{gathered}[/tex]AnswerThe old dot-matrix printer should take 52.8 minutes to print 12 pages.
a . Name all segments parallel to JK. b . Name all segments parallel to NS . c . Name a plane parallel to plane JKL . d . Name four segments skew to RQ .
a. Segments parallel to JK : OP ( because it is in front of JK and in the same direction).
b. Segments parallel to NS : RM, QL, JO, KP. ( because the lines are in the same direction).
c. plane parallel to plane JKL: OPQ ( because it is in front of JKL and in the same direction).
d. four segments skew to RQ: JO, PK, NS, SO. ( because these segments are neither parallel nor intersecting RQ).
Y=x^2-6x+2 in vertex form and show work
The vertex form is
[tex]Y=\mleft(x-3\mright)^2-7[/tex]The form of the equation given is: Y=ax^2+bx+c
So, a=1, b=-6 and c=2
The vertex form is
[tex]Y=a\mleft(x-h\mright)^2+k[/tex]Where
[tex]h=\frac{-b}{2a}\text{ , and k=f(h)}[/tex]Then
[tex]h=\frac{-b}{2a}=\frac{-(-6)}{2\cdot1}=3[/tex][tex]k=f(h)=f(3)=(3)^2-6\cdot3+2[/tex]Then, using a,h and k:
[tex]Y=(x-3)^3-7[/tex]Conver 9°18'42" to a decimal number of degrees.Do not round any intermediate computations.Round your answer to the nearest thousandth.
To convert from degrees to decimal, we use the formula shown below:
[tex]DD=d+\frac{\min}{60}+\frac{\sec}{3600}[/tex]Where
DD is the decimal degree
d is the degree (whole) in original degree/min/sec given
min is the minutes
sec is the number of seconds
Now,
Given,
d = 9
min = 18
seconds = 42
We substitute and find out the answer:
[tex]\begin{gathered} DD=d+\frac{\min}{60}+\frac{\sec}{3600} \\ DD=9+\frac{18}{60}+\frac{42}{3600} \\ DD=9+0.3+0.011666 \\ DD=9.311666 \end{gathered}[/tex]Rounding the answer to nearest thousandth (3 decimal places):
DD = 9.312Instructions: Determine the correctly sketched graph that matches the scenario.
ANSWER
The first graph.
EXPLANATION
We want to identify the correctly sketched graph for the scenario given.
The graph is to represent the motion of the ball as it is thrown in the air. This means that the graph must open downward since its vertex must be a maximum.
The ball is at a height of 4 feet when it leaves the hand of the thrower. This means that when the time is 0 seconds, the ball is at 4 feet. This signifies the y-intercept of the graph.
In other words, the y-intercept of the graph is 4 ft.
The maximum height reached by the ball is 6.25 feet and this occurs after 1.5 seconds. This represents the maximum of the graph i.e. the vertex of the graph.
In other words, the vertex of the graph is at (1.5, 6.25)
Therefore, we see that the graph that correctly contains the correct information is the first graph. That is the answer.
The diagram represents a lamp that Anderson wants to paint. He only wants to paint the lateral sides of the lamp.What is the area of the lateral surfaces that Anderson wants to paint?
Given the diagram of the lamp that Anderson wants to paint, you can identify that it is a rectangular prism.
The formula for calculating the Lateral Surface Area of a rectangular prism is:
[tex]LSA=Ph[/tex]Where "P" is the perimeter of the base and "h" is the height of the rectangular prism.
In this case, you can determine that:
[tex]\begin{gathered} P=6in+4in+6in+4in=20in \\ h=8in \end{gathered}[/tex]Therefore, substituting values into the formula and evaluating, you get:
[tex]LSA=(20in)(8in)=160in^2[/tex]Hence, the answer is: Second option.
Let X be a random variable with the following distribution. If E(X) = 108, then x2=
To obtain the value of x2, the following steps are necessary:
Step 1: Recall the formula for E(X) from probability theory, as follows:
From probability theory:
[tex]E(X)=\sum ^n_{i=1}X\cdot P(X)=X_1\cdot P(X_1)+X_2\cdot P(X_2)+\cdots+X_n\cdot P(X_n)[/tex]Step 2: Apply the formula to the problem at hand to obtain the value pf x2, as follows:
[tex]\begin{gathered} \text{Given that:} \\ E(X)=108 \\ X_1=80,P(X_1)=0.3 \\ X_2=?,P(X_2)=0.7 \end{gathered}[/tex]We now apply the formula, as below:
[tex]\begin{gathered} E(X)=\sum ^2_{i=1}X\cdot P(X)=X_1\cdot P(X_1)+X_2\cdot P(X_2) \\ \text{Thus:} \\ E(X)=X_1\cdot P(X_1)+X_2\cdot P(X_2) \\ \Rightarrow108=(80)\times(0.3)+X_2\times(0.7) \\ \Rightarrow108=24+X_2\times(0.7) \\ \Rightarrow108-24=X_2\times(0.7) \\ \Rightarrow84=X_2\times(0.7) \\ \Rightarrow X_2\times(0.7)=84 \\ \Rightarrow X_2=\frac{84}{(0.7)}=120 \\ \Rightarrow X_2=120 \end{gathered}[/tex]Therefore, the value of x2 is 120
What is the length of the missing leg? Could anybody help
In the given right triangle
Applying the Pythagorean Theorem
[tex]53^2=b^2+45^2[/tex]Solve for b
[tex]\begin{gathered} b^2=53^2-45^2 \\ b^2=784 \\ b=28\text{ ft} \end{gathered}[/tex]