PR = 10 and PQ = 4 QR
QR is the difference between PR and PQ . Hence
QR = 10 - 4
= 6
Given that sine = 0.87, using sin²0 + cos²0 = 1,
find cose (in Quadrant I). Show all your work for
credit - answer given to three decimal
approximation.
Work Shown:
[tex]\sin^2(\theta)+\cos^2(\theta)=1\\\\\cos^2(\theta) = 1-\sin^2(\theta)\\\\\cos(\theta) = \sqrt{1-\sin^2(\theta)} \ \ \ \text{.... cosine is positive in Q1}\\\\\cos(\theta) = \sqrt{1-(0.87)^2}\\\\\cos(\theta) \approx 0.4930517\\\\\cos(\theta) \approx 0.493\\\\[/tex]
What Is the difference between 4×3 and 4^3 ? Prove your answer with the equations AND explain your thinking.
The given expressions are
4×3 and 4^3
4 x 3 means 4 multiplied by 3 and the result is 12
4^3 means 4 raised to the power of 3 and this means
4 muliplied by 4 multiplied by 4. Thus, we have
4 x 4 x 4 = 64
What is the slope of the line segment?15129601 2 3 4 50-30-303
Ok, so:
To find the slope of the segment, we have to take two points:
Let's take: A(2,6) and B(1,3).
We calculate the slope as this:
m =( ( y2 - y1 ) / ( x2 - x1 )).
Where A( x1, y1) and B( x2, y2) are the points we took.
Then, m = (3 - 6) / (1-2), this is m = -3/-1, and that's equal to m=3
The average gas price in 2013 was $3.34. The probability that a gas price was less than $2.90 was 20%. What would be the standard deviation?
We know that the probability in a normal distribution can be obtained by the z score, the z score is given as:
[tex]Z=\frac{x-\mu}{\sigma}[/tex]where mu is the mean and sigma is the standard deviation. In this case we have:
[tex]\begin{gathered} P(X<2.9)=0.2 \\ P(Z<\frac{2.9-3.34}{\sigma})=0.2 \\ P(Z<\frac{-0.44}{\sigma})=0.2 \end{gathered}[/tex]Now, to have 20% (that is 0.2) we need that the z score to be -0.842, then we have:
[tex]\begin{gathered} -\frac{0.44}{\sigma}=-0.842 \\ \sigma=\frac{-0.44}{-0.842} \\ \sigma=0.52256532 \end{gathered}[/tex]Therefore the standard deviation is $0.52
Help please. I’ve had health issues recently and i’m trying to catch up on work and learn it. Thank you so much
80 mililiters of the 10% solution
120 mililiters of the 30% solution
Explanation:
let the amount of solution for the 10% = x
let the amount of solution for the 30% = y
The sum of the amount for the mixture of 10% solution and amount for the 30% solution = 200 mililiters
x + y = 200 ...(1)
In terms of fraction for each solution:
fraction of the 10% solution + fraction of the 30% solution = fraction of the mixture
percentage of the solution of the mixture = 22%
fraction of the 10% solution = 10% (x) = 0.1(x) = 0.1x
fraction of the 30% solution = 30%(y) = 0.3(y) = 0.3y
fraction of the mixture = 22%(200) = 0.22(200)
substitute the above into the equation for fraction:
0.1x + 0.3y = 0.22(200)
0.1x + 0.3y = 44 ...(2)
combine both equatons:
x + y = 200 ...(1)
0.1x + 0.3y = 44 ...(2)
Using substitution method to solve the equations:
from equation 1, let's make x the subject of formula:
x = 200 - y
substitute for x in equation (2):
0.1(200 - y) + 0.3y = 44
20 - 0.1y + 0.3y = 44
20 + 0.2y = 44
0.2y = 44 - 20
0.2y = 24
divide both sides by 0.2:
0.2y/0.2 = 24/0.2
y = 120
sustitute for y in equation (1):
x + 120 = 200
x = 200 - 120
x = 80
Hence, James must mix:
80 mililiters of the 10% solution
120 mililiters of the 30% solution
g(x)=14-2/3x and h(x)= -x-7
Solve g(9)+h(-14)
The value of the addition function is found as g(9) + h(-14) = 565/27.
What is defined as the domain of the function?A is a mathematical entity that accepts input, relates a rule to it, and returns the result. The domain of a function is the collection of all its inputs. Its codomain is the collection of all possible outputs. The range refers to the outputs which are actually used.For the given question,
The functions are given as;
g(x)=14-2/3x and h(x)= -x-7
Find the value of the function for the given domain of g(9) and h(-14).
g(9); Put x = 9 in g function.
g(9) = 14-2/3×9
g(9) = 376/27
h(-14); Put x = -14 in function h.
h(-14) = -x-7
h(-14) = -(-14)-7
h(-14) = 7
Now, add both values;
g(9) + h(-14) = 376/27 + 7
g(9) + h(-14) = 565/27
Thus, the value of the addition function is found as g(9) + h(-14) = 565/27.
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Mikaela has been tracking her basketball stats for the last week. She started shooting hoops today having already made 3200 baskets thisweek. She tracks how many baskets she has made in the next 30 minutes. If she continues shooting, how many baskets will she have made ifshe continues for one hour today? Write a linear equation with the variablet for time, then solve for the number of baskets.start 320010 min 322520 min 325030 min 327540 min 3300
Given:
Mikaela has been tracking her basketball stats for the last week.
We need to write a linear equation with the variable t for time
Let the equation has the form: y = m * t + b
Where y is the number of baskets she has made
She started shooting hoops today having already made 3200 baskets this
week.
so, at t = 0 , y = 3200
so, the value of b = 3200
We will find the value of m using the given table:
start 3200
10 min 3225
20 min 3250
30 min 3275
40 min 3300
So, the value of m = (3250 - 3225)/(20 - 10) = 25/10 = 2.5
So, the equation will be:
[tex]y=2.5t+3200[/tex]Now, we will find how many baskets will she have made if
she continues for one hour today?
So, we will substitute with t = 60 min into the last equation
So,
[tex]y=2.5\cdot60+3200=3350[/tex]So, she will make 3350 baskets
a offers three kinds of meat toppings and 17 * a vegetable topping and how many different ways could you select a meat topping or a vegetable topping
Since this restaurant offers three types of meat toppings and seventeen types of vegetable toppings we can use the fundamental counting principle to determine the number of possible outcomes. This is done below:
[tex]3\cdot(17)=51[/tex]We could select 51 possible combinations of meat and vegetable toppings.
Please Help. Functions and Relations. What is the effect on the graph of f(x)= x^2 when it is transformed to h(x)= 2x^2 + 15??
In general, given a function g(x), a vertical stretch/compression is given by the transformation below
[tex]\begin{gathered} g(x)\rightarrow a*g(x) \\ a>1\rightarrow\text{ stretch} \\ 0Therefore, in our case,[tex]x^2\rightarrow2x^2\Rightarrow\text{ vertical stretch by a factor of 2}[/tex]On the other hand, a vertical shift is given by the following transformation
[tex]\begin{gathered} g(x)\rightarrow g(x)+b \\ b>0\rightarrow\text{ b units up} \\ b<0\rightarrow\text{ b units down} \end{gathered}[/tex]Thus,
[tex]\begin{gathered} 2x^2\rightarrow2x^2+15=h(x)\Rightarrow\text{ 15 units up} \\ \end{gathered}[/tex]Hence, the answer is option C. Vertical stretch by a factor of 2 and a vertical shift by 15 units up.a sphere has a diameter of 3.5 inches what's the volume?
Solution
[tex]\begin{gathered} D\text{ = 3.5} \\ r\text{ = }\frac{D}{2}\text{ = }\frac{3.5}{2}\text{ = 1.75} \\ \text{Volume of a sphere = }\frac{4}{3}\times\pi\times r^2 \\ \text{ =}\frac{4}{3}\times\frac{22}{7}\times(1.75)^2^{} \\ \text{ =}\frac{26.95}{21}\text{ =12.83} \end{gathered}[/tex]Final Answer = 12.83
May I please get help with this. For I have tried many times to figure out the right answers
Explanation:
Two figures are congruent if they have the same size and shape. In this case, figure B is greater than figure A, so they are not congruent.
However, Figures C and D are congruent and we can map figure C to D by a rotation of 90 degrees counterclockwise about the origin. For example, the point (2, 3) of figure C becomes point (-3, 2), so the rule is
(x, y) ---> (-y, x) which is the rule for a 90 degrees rotation counterclockwise.
Answers:
Are figure A and B congruent? No
Which transformation maps A to B? None of these
Are figure C and D congruent? Yes
Which transformation maps C to D? Rotate figure C counterclockwise 90 about the origin.
Find the volume of the cone to the nearest 10th power you use 3.14 for pi. In the second box, take the exponent for the label.
The volume of a cone of radius r and height h is given by:
[tex]V=\frac{\pi r^2h}{3}[/tex]The cone in the figure has a radius of r = 2.1 cm and a height of h = 6.2 cm.
Substituting:
[tex]V=\frac{\pi\times\lparen2.1cm)^2\times6.2\text{ cm}}{3}[/tex]Using the value 3.14 for pi and calculating:
V = 28.62 cm 3
You should write 28.62 in the first box and 3 in the second box (for cubic cm)
guys whatd 3/2000 please help this is due by tomorrow
Answer:
0.0015
Step-by-step explanation:
don't forget to follow rate like
how do you find a vertex in intercept form
Quadratic functions can be written in vertex form, or
[tex]y=a\mleft(x-h\mright)^2+k[/tex]This is especially useful because the vertex of the function is found at the point (h, k).
We can find this form by completing squares, for instance, let y be:
[tex]y=x^2+bx+c[/tex]we can see that this equation is equal to
[tex]y=x^2+2(\frac{b}{2})x+(\frac{b}{2})^2-(\frac{b}{2})^2+c[/tex]because
[tex]2(\frac{b}{2})=b[/tex]and
[tex](\frac{b}{2})^2-(\frac{b}{2})^2=0[/tex]However, in this form, we can see that the first 3 terms are a perfect square, that is
[tex]x^2+2(\frac{b}{2})x+(\frac{b}{2})^2=(x+\frac{b}{2})^2[/tex]hence,
[tex]\begin{gathered} y=x^2+bx+c \\ y=(x+\frac{b}{2})^2-(\frac{b}{2})^2+c \end{gathered}[/tex]If we define
[tex]\begin{gathered} -(\frac{b}{2})^2+c=k \\ \text{and} \\ h=\frac{b}{2} \end{gathered}[/tex]we have that
[tex]y=(x+h)^2+k[/tex]the constant a arise when you have a leading term different from 1 in x^2.
Karen runs each lap in 7 minutes. She will run less than 63 minutes today. What are the possible numbers of laps she will run today? Use n for the number of laps she will run today. Write your answer as an inequality solved for n.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
time for each lap = 7 min
today's time run less than 63 min
n = # laps
Step 02:
1 lap ------- 7 min
n laps ------ 63 min
n laps * 7 min = 1 lap * 63 min
n laps < 63 min * lap / 7 min
n laps < 9 laps
The answer is:
She will run less than 9 laps .
-5m=8m-2 what solution? one solution.. two solutions... no solutions.. infinite solutions.. which solution?
Starting with the equation:
[tex]-5m=8m-2[/tex]Substract 8m from both sides:
[tex]\begin{gathered} -5m-8m=8m-2-8m \\ \Rightarrow-13m=-2 \end{gathered}[/tex]Divide both sides by -13:
[tex]\begin{gathered} \frac{-13m}{-13}=\frac{-2}{-13} \\ \Rightarrow m=\frac{2}{13} \end{gathered}[/tex]Therefore, the equation has one solution, which is:
[tex]m=\frac{2}{13}[/tex]which of the following is equivalent to the expression below? 3(5-2i)A. 15-2iB. 15-6iC. 8-2iD. 8-5i
ANSWER:
B. 15 - 6i
STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]3\left(5-2i\right)[/tex]We apply the distributive property and we are left with the following:
[tex]\begin{gathered} 3\left(5-2i\right)=3\cdot \:5-3\cdot \:2i \\ \\ 3\left(5-2i\right)=15-6i \end{gathered}[/tex]Therefore, the correct answer is B. 15 - 6i
divide the question(4.8x10^9)/(2.0x10^3)
We operate as follows:
[tex]\frac{4.8\cdot10^9}{2.0\cdot10^3}=2400000[/tex][tex]=2.4\cdot10^6[/tex]A slide of 4.1 meters long makes an angle of 27 degress with the ground. How high is the top of the slide above the ground? Round to the nearest hundreth meter.
Answer:
1.86 metres
Explanation:
Given the following
Length of the slide = 4.1m (hypotenuse)
Angle of elevation = 27 degrees
Required
Height of the slide above the ground
Using the trigonometry identity
sin theta = opposite/hypotenuse
sin 27 = H/4.1
H = 4.1sin27
H = 4.1(0.4539)
H = 1.86 metres
Hence the height ofthe slide above the pole is 1.86metre to the hundredth meters
Jenna can spend at most $200 on school clothes which inequality represents the amount that Jenna can spend on clothes
x is the quantity Jenna spend on clothes
[tex]x\le200[/tex]Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.y > x + 2y > - 2 x - 7
In order to determine a point that is part of the solution of the two given inequality, let's graph the two inequalities.
For both inequalities, they are already in a slope-intercept form y > mx + b where m = slope and b = the y-intercept.
For equation 1, y > x + 2, the y-intercept is 2 and slope is 1. Since the inequality is >, we will be using a broken line and the shade will be above the line.
The graph of inequality 1 is:
Moving on inequality 2, y > -2x - 7, the slope is -2 and the y-intercept is -7. Since the inequality symbol is >, we will be using a broken line on its border and the shade will be above the line.
The graph of inequality 2 is:
Combining the two graphs in one coordinate plane, we have:
The solution set of the given system of inequalities will be the common shaded area of both inequalities. There are infinite solutions for this.
We can get some coordinates from this common shaded area and this could be:
These coordinates can be (-3, 2), (-4, 3), (-2, 4), or (-2, 2).
We can also infer from the graph that the value of x is infinite however, the value of y must be greater than -1.
you pick a card at random and put it back and then pick another card at random what is the probability of picking an even number and then picking a five
STEP - BY - STEP EXPLANATION
What to find?
The probability of picking an even number and then picking a five.
Given:
Step 1
State the probability formula.
[tex]Probability=\frac{required\text{ outcome}}{all\text{ possible outcome}}[/tex]Step 2
Identify the even numbers and the all possible outcome.
Even numbers =4, 6
Step 3
Find each of the probability.
Let A be the event of picking an even number and B be the event of picking a 5.
[tex]\begin{gathered} P(A)=\frac{2}{4} \\ \\ P(B)=\frac{1}{4} \end{gathered}[/tex]Step 4
Determine the compound probability.
[tex]\begin{gathered} P(A\text{ and B\rparen=P\lparen A\rparen}\times P(B|A) \\ \\ =\frac{2}{4}\times\frac{1}{4} \\ \\ =\frac{2}{16} \\ \\ =\frac{1}{8} \end{gathered}[/tex]Step 5
Convert to percentage.
[tex]\begin{gathered} Probability=\frac{1}{8}\times\text{ 100\%} \\ \\ =12.5\text{ \%} \end{gathered}[/tex]ANSWER
12.5 %
Find the Least Common Denominator of 1/4 and 5/6
Answer:
The Least Common Denominator of 1/4 and 5/6 is 12
Explanation:
The Least Common Denominator (LCD) of two fractions is smallest number that can be common denominator for the set of fractions.
Given 1/4 and 5/6
The denominators are:
4 and 6
Let us break each numbers down into multiplications of prime numbers
4 = 1 * 2 * 2
6 = 1 * 2 * 3
So, the LCD is: 1 * 2 * 2 * 3 = 12
Use the factor theorem to determine if( x - 2) + (x + 4) are factors of the function below
Here, the dividend is x^3-6x^2+11x+6 and the divisor is x-2.
Put the value of divisor as 0 implies,
[tex]\begin{gathered} x-2=0 \\ x=2 \end{gathered}[/tex]Find f(2) implies,
[tex]\begin{gathered} f(2)=2^3-(6\times2^2)+(11\times2)-6 \\ =8-24+22-6 \\ =0 \end{gathered}[/tex]Therefore, x-2 is a factor of the polynomial.
Pu the value 0 for x+4 gives,
[tex]\begin{gathered} x+4=0 \\ x=-4 \end{gathered}[/tex]Find f(-4) gives,
[tex]\begin{gathered} f(-4)=(-4)^3-(6\times(-4)^2)+(11\times-4)-6 \\ =-64-96-44-6 \\ =-210 \end{gathered}[/tex]Therefore, x+4 is not a factor of polynomial.
Hence, Option C.
kamFind the area of the shaded sector.Round to the nearest tenth.167°17.8 ydArea = [ ? ]yd?Enter
We know the area of a cirlce is
[tex]A=\pi\cdot r^2[/tex]This is because, in radians, the angle of a whole circle is
[tex]2\pi[/tex]In order to proceed, we'll use the formula
[tex]167\cdot\frac{\pi}{180}\approx2.9147[/tex]Using this new value, we can now compute the area of the shaded region using the formula
[tex]A=\alpha r^2[/tex][tex]\text{Where }\alpha\text{ is the angle that generates the shaded region in radians}[/tex]In this case we have:
[tex]A=2.9147\cdot(17.8)^2=\text{ }923.493548[/tex]Round to the nearest tenth:
[tex]A=923.5yd^2[/tex]Given the triangle ABC at points A = ( 1, - 4 ) B = ( 4, - 5 ) C = ( 6, - 3 ), and if the triangle is first reflected over the y axis, and then over the x axis, find the new point A''.
Given: The coordinates of triangle ABC as
[tex]\begin{gathered} A=(1,-4) \\ B=(4,-5) \\ C=(6,-3) \end{gathered}[/tex]To Determine: The coordinates of triangle ABC after first reflect over the y-axis and then over the x-axis
Solution
The reflection over the y-axis rule is given as
[tex](x,y)\rightarrow(-x,y)[/tex]Let us apply the rule to the given triangle ABC
[tex]\begin{gathered} A(1,-4)\rightarrow A^{\prime}(-1,-4) \\ B(4,-5)\rightarrow B^{\prime}(-4,-5) \\ C(6,-3)\rightarrow(-6,-3) \end{gathered}[/tex]The reflection rule over the x-axis is given as
[tex](x,y)\rightarrow(x,-y)[/tex]Let us apply the rule to the given
[tex]\begin{gathered} A^{\prime}(-1,-4)\rightarrow A^{\prime}^{\prime}(-1,4) \\ B^{\prime}(-4,-5)\rightarrow B^{\prime}^{\prime}(-4,5) \\ C^{\prime}(-6,-3)\rightarrow C^{\prime}^{\prime}(-6,3) \end{gathered}[/tex]Hence, the new point of A'' = (-1, 4)
Solve 3n - 5p + 2n = 10p for n.
Solving for n ,
[tex]\begin{gathered} 3n-5p+2n=10p \\ \rightarrow3n+2n=10p+5p \\ \rightarrow5n=15p \\ \rightarrow n=\frac{15p}{5} \\ \\ \Rightarrow n=3p \end{gathered}[/tex]Sally has 71 peppermints. Bernard has p fewer peppermints than Sally. Write an expression that shows how many peppermints Bernard has.
an expression is:
y = 71 - p
Question is shown in image below. Answer format is also shown in image.
For |2x-7|>1:
This absolute value inequality results in two inequalities: 2x-7>1 or 2x-7<-1.
Solve these inequalities to find the answer:
[tex]\begin{gathered} 2x-7>1 \\ 2x>1+7 \\ x>\frac{8}{2} \\ x>4 \end{gathered}[/tex][tex]\begin{gathered} 2x-7<-1 \\ 2x<-1+7 \\ x<\frac{6}{2} \\ x<3 \end{gathered}[/tex]It means that the answer is x>4; x<3.
For |2x-7|<1:
This results in one complex inequality: -1<2x-7<1.
Solve it to find the answer:
[tex]\begin{gathered} -1<2x-7<1 \\ -1+7<2x<1+7 \\ 6<2x<8 \\ \frac{6}{2}It means that the answer is 3For |2x-7|=1:From the equation we can conclude that 2x-7=1 or 2x-7=-1.Solve these equations to find the answer:[tex]\begin{gathered} 2x-7=1 \\ 2x=1+7 \\ x=\frac{8}{2} \\ x=4 \end{gathered}[/tex][tex]\begin{gathered} 2x-7=-1 \\ 2x=-1+7 \\ x=\frac{6}{2} \\ x=3 \end{gathered}[/tex]The answer is x=3; x=4.write each measure in radians and express the answer in terms of π4. 315 degrees 5. -450 degrees
The equivalent measure of (315) degrees in radians will be (7π/4) rads.
As per the question statement, we are provided with an angular measure of 315 in the units of degrees,
And we are required to convert the above mentioned angular measure into it's equivalent unit of radians.
To solve this question, first we need to know about the relation between the two units of angular measure, degrees and radians, which goes as,
[180° = (π) rads]
Now using the unitary method and the above conversion reference point, we get,
[180° = (π) rads]
Or, [1° = (π/180) rads],
And, [315° = {(π/180) * 315} rads]
Or, [315° = {π * (315/180)} rads]
Or, 315° = [π * {(5 * 7 * 3 * 3)/(3 * 3 * 4 * 5)} rads]
Or, [315° = {π * (7/4)} rads]
Or, [315° = (7π/4) rads]
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