Given,
Solve for the variable,
[tex]1-p=7[/tex]Solution:
Take the variable on one side of the equation and the constant on another side of the equation.
[tex]\begin{gathered} -p=7-1 \\ -p=6 \\ p=-6 \end{gathered}[/tex]Thus, the value of p is -6.
The radius of a circle is 3 inches. What is the measure, in radians, of the angle subtended by an arc 3π inches long
ANSWER
[tex]\theta\text{ = }\pi\text{ radians}[/tex]EXPLANATION
We are given that the radius of the circle is 3 inches and the length of the arc that subtends the angle is 3π inches.
We can find the angle subtended by the arc by using the formula for length of an arc:
[tex]\begin{gathered} L\text{ = }\frac{\theta}{2\pi}\cdot\text{ 2}\pi R \\ \text{where }\theta\text{ = angle subtended, in radians} \\ R\text{ = radius} \end{gathered}[/tex]Therefore, we have that:
[tex]\begin{gathered} 3\pi\text{ = }\frac{\theta}{2\pi}\cdot\text{ 2}\cdot\pi\cdot3 \\ \Rightarrow3\pi\text{ = }\theta\cdot\text{ 3} \\ \text{Divide through by 3:} \\ \theta\text{ = }\pi\text{ radians} \end{gathered}[/tex]That is the angle subtended by the arc.
A figure has vertices (2,1), (5,1), and (2,4). What are the coordinates of the vertices of the nee figure when it is reflected over the y-axis
The co-ordinates when reflected over the y-axis are (-2,1), (-5,1) and (-2,4).
The co-ordinates of the figure given are (2,1), (5,1), and (2,4). It is clear that the figure is a triangle as (2,1) and (2,4) has same x-co-ordinates and (2,1) and (5,1) has same y-co-ordinates.
So this figure is reflected over the y-axis and we need to find the co-ordinates of the new transformed figure.
The reflection over y-axis does not change the y-co-ordinates but the x-co-ordinates are changed into their corresponding opposite signs. That is,
x ----> -x.
So the reflection over y-axis can be represented as (x, y) ----> (-x, y)
Hence the co-ordinates of the reflected figure are:
(-2,1), (-5,1), and (-2,4).
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Which class has 40% girls? Class A: 40 out of 110 Class B: 100 out of 140 Class C: 48 out of 120 Class D: 42 out of 100
Answer:
C
Step-by-step explanation:
Just divide 48/120.
I=$14,400 R=8% T=30 years Find p
Using simple interest, we know that the principal (p) is $6000.
What is simple interest?Simple Interest (S.I.) is a way for figuring out how much interest will accrue on a specific principal sum of money at a certain rate of interest.OR
Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.Using simple interest formula, we have:
|interest = $14,400Rate = 8% or 0.08Time = 30 yearsInterest = PRTTo find a principal we have
Principal = I/RTP = 14400/0.08(30)= 14000/2.4= 6000Hence the value of the principal or p is $6000.
Therefore, using simple interest, we know that the principal (p) is $6000.
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What is the volume of a cone with 80 km and 21 km?
The volume of the cone is 36,960km³.
What is a cone?
A cone is a three-dimensional solid geometric shape having a circular base and a pointed edge at the top called the apex.
The volume of a cone defines the space or the capacity of the cone. It is calculated using:
Vol. of a cone=1/3×π×r²h
where π=22/7
r = raπius of the base of the cone
h= height of the cone
Thus, vol. of the cone=1/3×22/7×21²×80
= 776160/21
=36,960km³
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Use the Associative Property of Multiplication to find the missing number: CATEL 4 x (5 x 3) = ( _x 5) x 3
Notice that the first number is 4, that would be the missing number.
The complete expression is
[tex]4\times(5\times3)=(4\times5)\times3[/tex]Remember that the associative property just groups the numbers differently.
data collected for a study involving IQ scores of four year old girls produced a mean of 100 and a standard deviation of 10 what IQ score does a z-score of -1.5 represent
Answer:
85
Explanation:
First, recall the formula for Z-Score.
[tex]Z-\text{Score}=\frac{X-\mu}{\sigma}\text{ where }\begin{cases}X=\text{raw score} \\ \mu=\operatorname{mean} \\ \sigma=\text{standard deviation}\end{cases}[/tex]Substitute the given values:
[tex]\begin{gathered} -1.5=\frac{X-100}{10}\text{ } \\ X-100=-1.5\times10 \\ X-100=-15 \\ X=100-15 \\ X=85 \end{gathered}[/tex]A z-score of -1.5 represents an IQ score of 85.
Write the following expression in logarithmic form.a^x = y
Explanation
Given
[tex]a^x=y[/tex]Therefore;
Answer:
[tex]x=\log_ay[/tex]The point (a,b) is reflected across the line y=x and then across the x-axis. Which of the following are the coordinates of its final image point in terms of a and b?(1) (-b,-a)(2) (-b,a)(3) (b,-a)(4) (-a,-b)
When a point is reflected across the line, y = x, the x and y coordinates changes places. Given that the coordinates of the original point is (a, b), the coordinate of the new point would be (b, a)
Again, this new point was reflected across the x axis. Recall, if reflection is done across the x axis, the sign of the x coordinate remains the same while the sign of the y coordinate is reversed,
Therefore, the coordinates of its final image point in terms of a and b is (b, - a)
The correct option is number 3
The function f(x) is a quartic function and a limited table of values is provided below. Write the equation of the quartic polynomial in standard form
This is the chart ~~
x ---- y
-5 768
-4 0
-3 -192
-2 -120
-1 0
0 48
1 0
2 -72
3 0
4 480
Using the Factor Theorem, the equation of the quartic polynomial in standard form is given by:
y = 4(x^4 + x³ - 13x² - x + 12).
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots(also called zeros) [tex]x_1, x_2, \codts, x_n[/tex] is given by the rule given as follows:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient of the polynomial, determining if it is positive(a positive) or negative(a negative).
From the given table, the roots are given by the values of x when y = 0, hence they are given by:
[tex]x_1 = -4, x_2 = -1, x_3 = 1, x_4 = 3[/tex]
Hence the function is given by:
f(x) = a(x + 4)(x + 1)(x - 1)(x - 3)
f(x) = a(x² + 5x + 4)(x² - 4x + 3)
f(x) = a(x^4 + x³ - 13x² - x + 12).
From the table, we also have that when x = 0, y = 48, hence the leading coefficient a can be found as follows:
12a = 48
a = 48/12
a = 4.
Hence the equation is:
y = 4(x^4 + x³ - 13x² - x + 12).
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24. lim
x-(1/2)-
|2x - 1|
2x - 1
After evaluating the limit we have came to find that the limit of [tex]\lim_{x\rightarrow \left(1/2)^-} $$|2x-1| 2x-1[/tex] as x approaches 1/2- is -1.
What is limit?In mathematics, a limit is the value that a function, sequence, or index approaches as an input or as an index approaches a specific value. Limits, which are fundamental to calculus and mathematical analysis, are required for the definitions of continuity, derivatives, and integrals.
The concept of a limit of a sequence is further generalized to include the concept of a limit of a topological network, in addition to having a connection to the category theory concepts of limit and direct limit.
A function's limit is typically expressed in formulas as
[tex]{\displaystyle \lim _{x\to c}f(x)=L}[/tex]
We need to solve the given equation
⇒ [tex]\lim_{x\rightarrow \left(1/2)^-} $$|2x-1| 2x-1[/tex]
⇒ [tex]\lim_{x\rightarrow \left(1/2)^-} $$(2\times|2x-1| x) + \lim_{x\rightarrow \left(1/2)^-}}$$( -1)[/tex]
⇒ Evaluate for x
⇒ [tex]0+ \lim_{x\rightarrow \left(1/2)^-}}$$( -1)[/tex]
⇒ 0 - 1
⇒ -1
Thus, after evaluating the limit we have came to find that the limit of [tex]\lim_{x\rightarrow \left(1/2)^-} $$|2x-1| 2x-1[/tex] as x approaches 1/2- is -1
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The equation (y + 2) = –1/3(x – 4) is in point-slope form. Fill in the blanks below to describe how to graph the equation.Plot the point _______, then move _______ unit(s) down and _______ unit(s) to the right to find the next point on the line. Question 1 options:(2, 4), one, three(–2, 4), one, three(4, –2), one, three(4, –2), three, one
1) In this question, we can see that a point has been given. So let's plot that point that belongs to the function:
We can tell that this point is part of the function by plugging it into the given function:
[tex]\begin{gathered} \mleft(y+2\mright)=-1/3\mleft(x-4\mright) \\ -2+2=-\frac{1}{3}(4-4) \\ 0=-\frac{1}{3}(0) \\ 0=0True \end{gathered}[/tex]2) So let's plot the graph:
Now, we can find another point by moving one unit down and three to the right.
3) Thus, the answer is:
[tex](4,-2)one,three[/tex]9. Bev had 24 pieces of candy. She gave Jamie 1/3 From the candy pieces remaining she the gave Selena 1/4. How many pieces of candy does she have left?
Number of candy's Bev has left with her is 12 .
What is equation?.Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given:
No. of candy Bev has= 24
She gave 1 /3 of candy to Jamie.
No. of candy Jamie got = 1 /3 of total candy
= 1 /3 * 24
= 8 candy
No. of candy she remained = total no. of candy - no of candy she gave to Jamie:
=24 - 8
=16
No. of candy Selena got = 1 /4 of remaining candy
=1 /4 ×16
=4
No. of candy left = total candy - (candy Jamie got +candy Selena got)
= 24-(8+4)
= 12 candy
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A soccer ball is kicked in the air such that its height, h, in metres, after t seconds can be modeled by the function h(t) = -4.9t^2 + 12t + 0.5
a) Determine the average rate of change of the height of the ball from 1s to 3s.
b) Estimate the instantaneous rate of change at 3s.
Part a: Average rate of change = 7.2 m/sec(going downward)
part b: Instantaneous rate of change = -7.6 m/sec
What is termed as the average rate of change?The average rate of change is indeed the rate during which one value changes in relation to another within a function. The slope of a plotted function is usually calculated using the average rate of change.The instantaneous rate of change is the rate change at a specific instant, and it is the same as the derivative value change at a specific point.For the given question;
The height of ball kicked is given by equation;
h(t) = -4.9t^2 + 12t + 0.5
Where, h(t) = -4.9t^2 + 12t + 0.5
Part a: Average rate of change of the height of the ball from 1s to 3s.
For t = 1 sec
h(1) = -4.9(1)^2 + 12(1) + 0.5
h(1) = 7.6 m
For t = 3 sec
h(3) = -4.9(3)^2 + 12(3) + 0.5
h(3) = -7.6
Average rate of change = -7.6 - 7.6 m/3 - 1
Average rate of change = - 15.2/2
Average rate of change = 7.2 m/sec(going downward)
Part b : instantaneous rate of change at 3s.
h(3) = -4.9(3)^2 + 12(3) + 0.5
h(3) = -7.6
instantaneous rate of change = -7.6 m/sec
Thus, the instantaneous rate of change of the ball at 3s -7.6 m/sec.
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Figure I and Figure Il are similar Which proportion must be true?
We know that figure I and figure II are similar, which means that:
-The corresponding angles are equal
-The corresponding sides are at the same ratio.
The ratios between the corresponding sides are:
[tex]\frac{15}{5}=\frac{12}{4}=\frac{8}{2}=\frac{x}{y}[/tex]You have to compare the determined ratios with the given options to find the true statement.
The only given proportion that is true is the first one
[tex]\frac{x}{y}=\frac{8}{2}[/tex]Hello. Is it possible to get help with this question (Math 9.11 Solving Logarithmic Equations)
answer: x = 3.27
A point on the rim of a wheel moves with a velocity of 95 feet per second. Find the angular velocity of the point if the diameter of the wheel is 5 feet.
To find:
The angular velocity of the point.
Solution:
Given the wheel moves with a velocity of 95 feet per second and the diameter is 5 feet.
So, the radius of the wheel is 5/2 feet.
The formula used to find the angular velocity of the wheel is given by:
[tex]\omega=\frac{v}{r}[/tex]So, by the given information is:
[tex]\begin{gathered} \omega=\frac{95}{\frac{5}{2}} \\ \omega=38 \end{gathered}[/tex]Thus, the angular velocity is 38 radians per second.
Graph a line that contains the point 1 (4,3) and has a slope of 2 y 6- 4- 2 х -6 -4 2 4 6 -4 -6
To solve the exercise you can use the point-slope formula, that is,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{ Where m is the slope of the line and} \\ (x_1,y_1)\text{ is a point through which the line passes} \end{gathered}[/tex]So, in this case, you have
[tex]\begin{gathered} m=\frac{1}{2} \\ (x_1,y_1)=(4,3) \end{gathered}[/tex][tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{ Replace} \\ y-3=\frac{1}{2}(x-4) \\ y-3=\frac{1}{2}x-\frac{1}{2}\cdot4 \\ y-3=\frac{1}{2}x-2 \\ \text{ Add 3 from both sides of the equation} \\ y-3+3=\frac{1}{2}x-2+3 \\ y=\frac{1}{2}x+1 \end{gathered}[/tex]Then,
Plot the point given in polar coordinates.Find three additional polar representations of the point, using −2 < < 2. (Enter your answers in order from smallest to largest first by r-value, then by -value.)
Correct graph: C
[tex]\begin{gathered} 1st\text{ alternative form:} \\ (-9,\frac{2}{3}\pi)\frac{}{} \\ 2nd\text{ alternative form:} \\ (9,\frac{5}{3}\pi) \\ 3rd\text{ alternative form:} \\ (-9,\frac{8}{3}\pi) \end{gathered}[/tex]
Find the y-intercept of the line on the graph.
The y-intercept of the given line on the graph is -3.
What is the y-intercept?A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis. This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points satisfy x = 0 because of this.So, the y-intercept of the given line:
Formula of slope: y = mx + bWhere m is the slope and b is the y-intercept.Let's now follow the graph's value of y at x = 0.
Now, according to the given graph (Graph is attached below).
When, x = 0 then, y = -3.Therefore, the y-intercept of the given line on the graph is -3.
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Nick bakes 3 dozen cookies for the bake sale. Each cookie requires 12 milliliters of water. How
many milliliters of water does he use?
In linear equation, 432 milliliters of water does he use .
What are a definition and an example of a linear equation?
An equation with only one variable is referred to as a linear equation in one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. A linear equation in one variable would be 9x + 78 = 18, for instance.With only a constant and a first-order (linear) term, a linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept.Nick bakes 3 dozen cookies for the bake sale.
1 cookie requires 12 milliliters of water.
water does he use = 3 × 12 × 12
= 432 milliliters of water
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Suppose that 3y - 5 = 45 and y = 3x - 2.Which of the following equations is equivalent to 3y - 5 = 45, but written only in terms of x?
We have
[tex]\begin{gathered} 3y-5=45 \\ y=3x-2 \end{gathered}[/tex]So we must replace the value of y of the second equation in the first equation
[tex]\begin{gathered} 3(3x-2)-5=45 \\ 9x-6-5=45 \\ 9x-6=45+5 \\ 9x-6=50 \end{gathered}[/tex]So, the answer is 9x - 6 = 50. Last option.
A population proportion is 0.20. A random sample of size 200 will be taken and the sample proportion will be used to estimate the population proportion. Use the z-table.
Round your answers to four decimal places.
a. What is the probability that the sample proportion will be within ±0.02 of the population proportion?
b. What is the probability that the sample proportion will be within 0.05 of the population proportion?
a. The probability that the sample proportion will be within ±0.02 of the population proportion - 0.5223
b. The probability that the sample proportion will be within 0.05 of the population proportion - 0.9232
[tex]Given, \\$P=0.2 a$ \\$n=200$ \\mean, \ $\mu \hat{p}=p$ \\$=0.20$ \\Standard deviation, $\sigma_p=\sqrt{\frac{p(1-p)}{n}}$ \\$=\sqrt{\frac{0.20(1-0.20)}{208}}$ \\$=\sqrt{\frac{0,20(0,80)}{200}}$ \\$=\sqrt{\frac{0.16}{200}}$. \\$=0.0283$ \\a) $p(|x-\mu|=\pm 0.02)=f\left(\frac{-|x-\mu|}{\sigma \hat{p}} < z < \frac{|x-\mu|}{\sigma_{\hat{p}}}\right)$ \\$=1\left(\frac{-0.02}{0.0283} < = < \frac{0.02}{0.0283}\right)$ \\$=P(-0,71 < z < 0,71)$[/tex]
[tex]$$\begin{gathered}=p(z < 0,71)-p(z < -0,71) \\=0,7612-0.2389 \\=0,5223 } \\\therefore P(|x-\mu|=\pm 0.021=0,5223)\end{gathered}$$[/tex]
[tex]b)\\$$\begin{aligned}p(|x-\mu|=\pm 0.05)=p\left(\frac{|x-\mu|}{\sigma \hat{p}} < z < \frac{|x-\mu|}{\sigma \hat{p}}\right) \\=p\left(\frac{-0.05}{0.0283}-z < \frac{0.05}{0.0283}\right) \\=& p(-1.77 < z < 1.77) \\=& P(z < 1.77)-p(z < -1.77) \\\therefore p(i x-\mu \mid&=\pm 0.05)=0.9232\end{aligned}$$[/tex]
What is the population ?A population is a complete group of individuals, regardless of whether that group consists of a nation or a group of people with a common characteristic.
In statistics, a population is a group of individuals from which a statistical sample is taken for research. Thus, any selection of individuals grouped together on the basis of some common characteristic can be called a population. A sample may also refer to a statistically significant portion of the population rather than the entire population. Therefore, statistical analysis of a sample must report the approximate standard deviation or standard error of the results for the entire population. Only the whole population analysis has no standard error
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What is a like terms to 15?a.15xb.5bc.22d.not enough information
Those are like terms because are constants
[tex]25,x,3x^2[/tex]Those aren't like terms because 25 is a constant, x is a variable, and 3x² is a quadratic variable
if you roll a dice twice, what is the possibility of getting a number less than 5 on both rolls?
Solution
Step 1
Write an expression for the probability of an event
[tex]\begin{gathered} \text{If an event is A} \\ P(A)\text{ = }\frac{No\text{ of required events}}{No\text{ of total possible events}} \end{gathered}[/tex]
No of the required events can be found with the following table
The numbers(1,2,3,4,5,6) on the vertical are for one dice and the others on the horizontal are for the second dice
No of required of numbers on both dices less than 5 are : 1,1 1,2 1,3 1,4 2,1 2,2 2,3 2,4 3,1 3,2 3,3 3,3 3,4 4,1 4,2 4,3 4,4. The number of the events are therefore, = 16
No of total events = 36
Step 2
Substitute the values and find the required probability
[tex]\text{Probability of getting numbers less than 5 on both dice = }\frac{16}{36}=\text{ }\frac{4}{9}[/tex]In the following diagram, segment QR is the image of segment NP after a dilation centered at the origin with a scale factor of k. Which of the following would not be a correct calculation of k.
The ratio OQ/QN would not give a correct calculation of K
Here, we want to select which of the options would be a wrong calculation for k which is the scale factor
Any of the ratios that would measure k should be such a ratio that compares similar distances
The correct answer in this case is OQ/QN
The reason why it is wrong is that while OQ meaures the distance from the center of dilation to the first segment, QN should also have measured a comparable distance
Thus, ON should have been what to use if we are to compare both distances since they would have measured the distances from the center of dilation which is the origin in this case
I need help with this question and can you please answer it how the paper says so I can understand it better
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given points
[tex]\begin{gathered} \text{ points of origin}=(0,0) \\ (3-2i)\text{ means that the start point}=(3,-2) \end{gathered}[/tex]STEP 2: Write the formula for finding the modulus
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{where (}x_{1,}y_1_{})=(0,0) \\ (x_2,y_2)=(3,-2) \end{gathered}[/tex]STEP 3: Substitute the values into the formula to get the answer
[tex]\begin{gathered} d=\sqrt[]{(3-0)^2+(-2-0)^2} \\ d=\sqrt[]{(3)^2+(-2)^2} \\ d=\sqrt[]{9+4} \\ d=\sqrt[]{13} \\ d=3.605551275 \\ d\approx3.6\text{ to the nearest tenth} \end{gathered}[/tex]Hence, the required modulus is approximately 3.6 to the nearest tenth.
The relationship between altitude and the boiling point of a liquid is linear. At an altitude of 8100 ft, the liquid boils at 198.61°F. At an altitude of 4500 ft, the liquid boils at 205.45°F. Write an equation giving the boiling point b of the liquid, in degrees Fahrenheit, in terms of altitude a, in feet. What is the boiling point of the liquid at 2400 ft?
Write an equation.
b=
Answer:
What is the relationship between altitude and boiling point of a liquid?
At a higher elevation, the lower atmospheric pressure means heated water reaches its boiling point more quickly—i.e., at a lower temperature. Water at sea level boils at 212 degrees Fahrenheit; at 5,000 feet above sea level, the boiling point is 203 degrees F. Up at 10,000 feet, water boils at 194 degrees F.
Step-by-step explanation:
Answer:
[tex]\textsf{Equation}: \quad b=-0.0019a+214[/tex]
209.44 °F
Step-by-step explanation:
Define the variables:
a = altitude, in feet.b = boiling point, in degrees Fahrenheit.Given:
At an altitude of 8100 ft, the liquid boils at 198.61°F. At an altitude of 4500 ft, the liquid boils at 205.45°F.If the relationship between altitude (a) and boiling point (b) is linear, this can be modelled as:
[tex]\boxed{b=ma+c}[/tex]
where:
a is the independent variable.b is the dependent variable.c is a constant.Find the slope of the linear equation by substituting the given ordered pairs into the slope formula:
[tex]\implies \textsf{slope}\:(m)=\dfrac{b_2-b_1}{a_2-a_1}=\dfrac{205.45-198.61}{4500-8100}=\dfrac{6.84}{-3600}=-0.0019[/tex]
Substitute the found slope and one of the ordered pairs into the point-slope formula:
[tex]\implies b-b_1=m(a-a_1)[/tex]
[tex]\implies b-205.45=-0.0019(a-4500)[/tex]
[tex]\implies b-205.45=-0.0019a+8.55[/tex]
[tex]\implies b=-0.0019a+214[/tex]
Therefore, an equation giving the boiling point (b) of the liquid in terms of altitude (a) is:
[tex]\boxed{b=-0.0019a+214}[/tex]
To find the boiling point of the liquid at 2400 ft, substitute a = 2400 into the found equation:
[tex]\implies b=-0.0019(2400)+214[/tex]
[tex]\implies b=-4.56+214[/tex]
[tex]\implies b=209.44[/tex]
Therefore, the boiling point of the liquid at 2400 ft is 209.44 °F.
700,000,000+60,000,000+8,000,000+90,000+20,000+50+4
700,000,000
+
60,000,000
+
8,000,000
+
90,000
+
20,000
+
50
+
4
____________
768,110,054
help please i really need this
Answer:
Solution examples: (5,0) and (5,5)
Not a Solution (1,5) and (5, 10)
Explanation:
The graph and the points inside and outside the solution set are given below.
The grey-blue region is the solution to the system and the region outside it is not.
Therefore, the point (5, 0) is a solution and (1, 5) is not a solution.
