Given the equation:
[tex]Q\mleft(t\mright)=500\mleft(1.3\mright)^t[/tex]The given function represents an exponential growth function
(a) The initial value is P, which will be the value when t = 0
So, P = 500
(b) The growth factor is a = 1.3 - 1 = 0.3
(c) The growth rate is p = 1.3
Which equation is equivalent to: 3r=90-5A. -3r=-90-5B. -3r=90+5C. 3r+5=90D. 3r=90+5
Answer
Option C is correct
3r + 5 = 90
Explanation
To solve this, we will simplify the given equation
3r = 90 - 5
Add 5 to both sides
3r + 5 = 90 - 5 + 5
3r + 5 = 90
Hope this Helps!!!
G04.01 Adjacent Angles Use the angle addition postulate to find the measure of the angle
1) 50 + 80 = 130
2) 115 + 58 = 173
3) 45 + 27 = 72
4) angle PQT
5) angle RQT
6) angle SQU
7) angle UQR
8) angle PQR
9) 10 degrees
10) 135 degrees
11) 100 degrees
12) 35 degrees
13) 90 degrees
14) 90 degrees
15) 125 degrees
16) 135 degrees
17) 45 degrees
18) 280 degrees
w1The equation of this line isy = 2x + 3. Which of thefollowing shows a way thatwe could change theequation to make the linesteeper?1 2 31-3 -2 -1-1-21NHA. y = 2x + 5B. y=-2x + 3C. y= 4x + 3
Solution
Draw a steeper graph for the equaton below:
[tex]y=2x+3[/tex]A higher positive slope means a steeper upward tilt to the curve, which you can see at higher output levels. A negative slope that is larger in absolute value (that is, more negative) means a steeper downward tilt to the line. A slope of zero is a horizontal line. A vertical line with an infinite slope
y = 4x + 3
Therefore the correct answer is
[tex]y=4x+3[/tex]Side AB in Triangle ABD corresponds to which side of triangle ABC
Given:
Three right angled triangle are given. Triangle ABC right angled at B , triangle BDC right angled at D and triangle ABD right angled at D.
The objective is to find which side of triangle ABC is correspond to the side AB in triangle ABD.
Consider the right angled triangle ABC right angled at B. So let's take AB as the base.
Also consider right angled triangle ABD right angled at D. So the side AD will be the base of the triangle.
Hence, side AD of triangle ABD is correspond to side AB of triangle ABC.
Find the values of A and B in Ax + By = 80 such that the equation is perpendicular to 14x + 35y = 70 and has the same y-intercept.
Two perpendicular lines have an opposite slope.
Then you have the next equation of the line:
[tex]14x+35y=70[/tex]You can find the slope and the y-intercept by turning this to a form slope-y-intercept (y=mx+b) by clearing the varible y:
1) find the probability the arrow will land on a multiple of 4 or 6 or both
Write out the number of elements in the sample space as we denote the sample space as S
[tex]n(S)=36[/tex]Write out the event space E1 for the multiples of 4
[tex]\begin{gathered} E_1=\mleft\lbrace4,8,12,16,20,24,28,32,36\mright\rbrace \\ n(E_1)=9 \end{gathered}[/tex]Write out the event space E2 for the multiples of 6
[tex]\begin{gathered} E_2=\mleft\lbrace6,12,18,24,30,36\mright\rbrace \\ n(S)=6 \end{gathered}[/tex]The probability that the arrow will land on a multiple of 4 or 6 or both will land can be represented thus
[tex]P(E_1)+P(E_2)+P(E_1\cap E_2)[/tex][tex]\begin{gathered} E_1\cap E_2=\mleft\lbrace12,24,36\mright\rbrace \\ n(E_1\cap E_2)=3 \end{gathered}[/tex][tex]P(E_1)=\frac{n(E_1)}{n(S)}=\frac{9}{36}=\frac{1}{4}[/tex][tex]P(E_2)=\frac{n(E_2)}{n(S)}=\frac{6}{36}=\frac{1}{6}[/tex][tex]P(E_1\cap E_2)=\frac{n(E_1\cap E_2)}{n(S)}=\frac{3}{36}=\frac{1}{12}[/tex]Therefore,
[tex]P(E_1)+P(E_2)+P(E_1\cap E_2)=\frac{1}{4}+\frac{1}{6}+\frac{1}{12}=\frac{3+2+1}{12}=\frac{6}{12}=\frac{1}{2}[/tex]Hence, the probability that the arrow will land on a multiple of 4or 6 or both is 1/2
Reasoning Find the sum (8x + 1) +(-9x + 7). Use pencil and paper. Explain how you know whento combine terms with variables.(8x+1)+(-9x + 7) = (simplify your answer.)
Let's begin by listing out the information given to us:
[tex]\mleft(8x+1\mright)+\mleft(-9x+7\mright)[/tex]We will open the bracket, we have:
[tex]8x+1-9x+7[/tex]Put like terms together, we have:
[tex]\begin{gathered} 8x-9x+1+7 \\ \Rightarrow-x+8 \end{gathered}[/tex]Therefore, (8x + 1) + (-9x + 7) = -x + 8
Vertex of parabola is (-4,5). One x intercept is (2,0). Find the other x intercept justify your response
Step 1. The vertex of the parabola is:
(-4,5)
And one of the x-intercepts i:
(2,0)
They are shown in the following diagram (not to scale):
Step 2. We are asked to find the other x-intercept. To find it, we use the symmetry of the parabola:
There must be the same distance between the vertex and each x-intercept.
To represent that distance we draw a triangle between the known vertex and x-intercept:
That triangle has a side of 5 and a side of 6 units.
Step 3. We draw the same triangle but to the left side of the vertex to find the other x-intercept:
We end up at (-10,0) this is the other x-intercept.
Answer:
(-10, 0)
Name the order pair for the point A.A) (3,4)B) (4,3)C) (0,3)D) (0,4)
B
1) Bearing in mind that in a coordinate pair, the first number refers to the x-coordinate as well as the second one refers to the y-coordinate, we can examine that point.
2) So, we can see that point A is located at x = 4, and y=3
3) Thus the answer is B
Measurement: Customary Units", then answer each of the following questions. Round answers to the nearest hundredth, if necessary.Q: If 1,760 yards = 1 mile, then 880 yards = ? miles.
If 1,760 yards = 1 mile, then 880 yards = ? miles.
Applying proportion
we have that
1/1,760=x/880
solve for x
x=880/1,760
x=0.50 milesYour older brother drove to your grandparents’ house in a different car but left from the same location at the same time. If he traveled at a constant speed of 60 miles per hour, explain why he would reach your grandparents’ house first. Use words, diagrams, or numbers to explain your reasoning? Why would he reach your grandparents house first?
Answer:
He could reach your grandparents hose first if he drove faster than the car you have been in.
For example, if the car you where on was traveling at a constant speed of 40 miles per hour, then he would get first.
what is the exact measure of central angle in radians?
The measure of the central angle is 2.5 rad
Explanation:Central angle is:
[tex]\frac{\text{Arc length}}{radius}[/tex]which is
[tex]\frac{5}{2}^{}[/tex]OR
2.5 rad
How do I figure out the measurements for the angle Q?s
ANSWER:
B) 33°
STEP-BY-STEP EXPLANATION:
We know that both triangles are congruent, therefore they have equal corresponding angles.
To determine which are the equal angles, we must place both triangles in the same way, just like this:
Now, we can better notice that the corresponding angle to Q is R, R measures 33°, therefore Q also measures 33°. Which means that the correct answer is B) 33°
I think of a number Then I multiply it by 3Then I add 4 Then I divide the answer by 4. My final answer is 3 less than the number I thought of at the beginning 1. Write down an algebraic equation that represents this problemSolve your equation to find the number Max started with. 2(a) Another think of a number' problem is represented by the equation below [tex]4( \frac{3w + 5}{4} + 2) - 3 = 5w[/tex]
Think of an unknown number "x".
multiply it by 3 --> 3 x
add 4 --> 3 x + 4
divide the answer by 4: --> (3 x + 4 ) / 4
this is 3 less than the original number:
(3 x + 4)/ 4 = x - 3 <== This is the equation that represents the problem
solve for "x", starting by multiplying by 4 both sides to get rid of the denominator on the left:
3 x + 4 = 4 x - 12
subtract 3 x from both sides to gather all the terms in 'x" on the right.
4 = 4 x - 3 x - 12
combine
4 = x - 12
add 12 on both sides:
16 = x <== this is the answer
Then the original number was x = 16
find the inverse of each of the following functions by first switching x and y and then solving for y[tex]y = ( \frac{1}{4}x + 6) ^{3} [/tex]
First we switch x and y:
[tex]x\text{ = (}\frac{1}{4}y+6)^3[/tex]Then we would solve for y:
[tex]\begin{gathered} \text{cube root both sides:} \\ \sqrt[3]{x}\text{ = }\sqrt[3]{(\frac{1}{4}}y+6)^3 \\ \sqrt[3]{x}\text{ = }\frac{1}{4}y+6 \\ \end{gathered}[/tex][tex]\begin{gathered} \sqrt[3]{x}\text{ -6= }\frac{1}{4}y \\ \sqrt[3]{x}\text{ -6 = }\frac{y}{4} \\ 4(\sqrt[3]{x}\text{ -6) = y} \end{gathered}[/tex][tex]y\text{ = 4(}\sqrt[3]{x}\text{ - 6)}[/tex]Brandon wants to package 51 of his books in boxes. He has different size boxes that each hold different quantities of books. Which of the box sizes below could he use to hold all of the books with none left over? Mark all that apply. 2 Ba 3 B11 17 D 21 E 27
51 books are to be packed into boxes without any book left over.
Clue to the answer is: identify the factors of 51 in the given options.
So, we have 3 and 17 because both can divide 51 without remainder.
Hence, the solutions to the question are; 3 (option A) and 17 (option C)
Tell whether x and y show direct variation. Explain your reasoning. If so, find k.x=2/5y
The relationship is;
[tex]x=\frac{2}{5}y[/tex]This shows DIRECT VARIATION
The constant involved here is;
[tex]x=ky[/tex][tex]k=\frac{2}{5}[/tex]What is the solution to the equation below? (Round your answer to twodecimal places)5ehx=35oA X=201B = 3.980C = 4220
The answer is A, x=2.01
Solve the system of linear equations by graphing. I need help with both.
7.
[tex]\begin{bmatrix}y=-\frac{2}{3}x+2\text{ clear blue} \\ y=\frac{1}{3}x+5\text{ dark blue}\end{bmatrix}[/tex]graphing
8.
[tex]\begin{bmatrix}4x-y=2\text{ clear blue} \\ x-y=-1\text{ dark blue}\end{bmatrix}[/tex]graphing
I have to enter into a program called goformative the interval notation for -1 < p < = -6. Another tutor said the answer is empty set or null set. I have tried entering this and it says it is wrong. Is there something missing?
The inequalities to solve are,
[tex]\begin{gathered} 7p+5\leq-37 \\ \text{and} \\ -10p<10 \end{gathered}[/tex]Solving the first inequality:
[tex]\begin{gathered} 7p+5\leq-37 \\ 7p\leq-37-5 \\ 7p\leq-42 \\ p\leq-\frac{42}{7} \\ p\leq-6 \end{gathered}[/tex]Solving the second inequality:
[tex]\begin{gathered} -10p<10 \\ \frac{-10p}{-10}>\frac{10}{-10} \\ p>-1 \end{gathered}[/tex]So, the solution is
[tex]\begin{gathered} p\leq-6 \\ \text{and} \\ p>-1 \end{gathered}[/tex]The graph of both solutions are shown below:
[tex]p\leq-6[/tex]Then,
[tex]p>-1[/tex]Now, recall that in interval notation, "(" and ")" indicates that an interval is not included, and "[" and "]" indicates that an interval is included.
We can write both solutions in interval notation as,
[tex]\begin{gathered} p\leq-6 \\ \text{and} \\ p>-1 \\ --------------- \\ \text{Interval Notation:} \\ (-\infty,-6\rbrack \\ \text{and} \\ (-1,\infty) \\ --------------- \\ (-\infty,-6\rbrack U(-1,\infty) \end{gathered}[/tex]Find the factors of f(x), given that x = 4 is a zero.f(x) = x^3 − 7x^2 + 2x + 40 A. (x − 4)(x + 5)(x − 2)b. (x + 4)(x + 5)(x − 2)c. (x − 4)(x − 5)(x + 2)d. (x + 4)(x − 5)(x + 2)
Let's determine the factors of the following function:
[tex]\text{f(x) = x}^3-7x^2\text{ + 2x + 40}[/tex]Since one of the factors is given, which is x = 4 or (x - 4), let's determine the quadratic function using synthetic division.
We get,
[tex]\text{f(x) = x}^3-7x^2+2x+40=(x-4)(x^2-3x-10)[/tex][tex]\text{ f(x) = (x - 4)(x + 2)(x - 5)}[/tex]Therefore, the answer is letter C : (x - 4)(x - 5)(x + 2)
Find the perimeter of the square shown belowArea49 cm?
Darnel's Health Foods makes a mixed nut blend that contains 19% cashews. Today, Joe, oneof the workers, needs to make 74 pounds of this mix. If he will be using one nut mix thatcontains 21% cashews and another that contains 16% cashews, how much of each should hecombine?Write your answers as whole numbers or as decimals rounded to the nearest tenth.
Let A be the amount of mix that contains 21% cashews and B the amount of mix that contains 16% cashews that will be used to create a mix with 19% cashews.
The total amount of mix will be A+B.
Notice that the total amount of cashews on that mix will be equal to:
[tex]\frac{19}{100}(A+B)[/tex]On the other hand, the total amount of cashews on the 21% mix, is:
[tex]\frac{21}{100}A[/tex]While the total amount of cashews on the 16% mix, is:
[tex]\frac{16}{100}B[/tex]Then:
[tex]\frac{21}{100}A+\frac{16}{100}B=\frac{19}{100}(A+B)[/tex]On the other hand, since the total amount of mix will be 74 pounds, then:
[tex]A+B=74[/tex]These two equations form a 2x2 system of equations. Solve the sistem to find A and B.
Isolate A from the first equation and substitute the expression into the second equation:
[tex]\begin{gathered} \frac{21}{100}A+\frac{16}{100}B=\frac{19}{100}(A+B) \\ \Rightarrow21A+16B=19A+19B \\ \Rightarrow21A-19A=19B-16B \\ \Rightarrow2A=3B \\ \Rightarrow A=\frac{3}{2}B \end{gathered}[/tex][tex]\begin{gathered} A+B=74 \\ \Rightarrow\frac{3}{2}B+B=74_{} \\ \Rightarrow\frac{5}{2}B=74 \\ \Rightarrow B=\frac{2}{5}\cdot74 \\ \Rightarrow B=29.6 \end{gathered}[/tex]Substitute the value of B into the expression of A to find A:
[tex]\begin{gathered} A=\frac{3}{2}B \\ =\frac{3}{2}(29.6) \\ =44.4 \end{gathered}[/tex]Therefore, 44.4 pounds of 21% cashews mix and 29.6 pounds of 16% cashews mix should be used to produce 74 pounds of 19% cashews mix.
I'm having a little trouble on how to do this type of math.
Given the expression:
[tex]60x-24[/tex]The greatest common factor between 60 and 24 is:
Now:
[tex]\begin{gathered} 60=12\cdot5 \\ 24=12\cdot2 \end{gathered}[/tex]Using this and factorizing the expression:
[tex]60x-24=12\cdot(5x-2)[/tex]Circle O is shown on the coordinate plane below. PQ is a diameter of circle O.What is the circumference of circle O? If necessary, round your answer to the nearest tenth.
Circunference of a circle is found by 2π • radius
In the image we see a circle with center in x=-3. y= 2
Radius of circle can be found , with the segment OQ or segment OP. Because both are radius
Also radius can be found with segment QP and dividing by 2. (QP/2 ).
Use the first way, finding OQ.
Then have to use Pithagoras teorem that says
X^2 + Y^2 = R^2
where X= x-x'. Y= y-y'. R = radius
so then O, the center has coordinates (-3, 2 )
and Q has coordinates. ( 3,5 )
replace O by ( x,y). And replace Q by (x',y')
then (x - x')^2 + (y - y')^2 = R^2
(-3-3)^2 + ( 2 - 5)^2 = R^2
(-6)^2 + (-3)^2 = R^ 2
36 + 9 = 45 = R^2
Its found R^2, now rest to find R = √45 = 6.708
Now that is found R ,lets find 2•π•R
2•π•R = 42.15
Determine if the following side lengths could form a triangle. Prove your answer with an inequality 6,18,14
For any triple of side measures a, b, c. We use the following inequality:
[tex]a+b>c[/tex]Therefore:
a = 6
b = 14
c = 18
[tex]\begin{gathered} 6+14>18 \\ 20>18 \end{gathered}[/tex]Thus, you can form a triangle.
Answer: Yes. The inequality is
[tex]6+14>18[/tex]Rewrite the following without an exponent. 2-4
Answer
2⁻⁴ = (1/16) = 0.0625
Explanation
When a variable is raised to the power of a negative number, this is the same as 1 over that variable raised to the positive value of that power.
So,
2⁻⁴ = (1/2⁴) = (1/16) = 0.0625
Hope this Helps!!!
Given that P(B|A)=0.76 and P(A)=0.46, what is P(B AND A)? Round to three decimal places.
Solution:
Given;
[tex]P(B|A)=0.76,P(A)=0.46[/tex]Thus, the probability of B and A can be calculated using the formula;
[tex]\begin{gathered} P(B\text{ and }A)=P(B|A)\times P(A) \\ \\ P(B\text{ and }A)=0.76\times0.46 \\ \\ P(B\text{ and }A)=0.3496 \\ \\ P(B\text{ and }A)\approx0.350 \end{gathered}[/tex]ANSWER:
[tex]P(B\text{and}A)=0.350[/tex]Jacquez is a scientist running a month-long experiment on the growth of E. Coli in warm and cool environments. He put cultures into 10 different petri dishes foreach environment. Below are the population sizes of each petri dish at the end of the experiment. 1. Compare the two data sets visually. Be sure to include your visuals and a discussion of measures of center and variability. 2. Find the measures of center and variability in the table. Be sure to show all your work.
Explanation:
Given that:
[tex]\begin{gathered} Warm:61,100,13,96,68,89,80,74,96,56 \\ Cool:53,7,73,4,70,82,73,40,50,10 \end{gathered}[/tex]1.
Graph 1 (Warm):
Graph 2 (Cool):
2. The measure of center and variability is shown below:
Mean:
[tex]\begin{gathered} \mu=\frac{\Sigma f(x)}{N} \\ \\ Warm \\ \begin{equation*} \mu=\frac{61+100+13+96+68+89+80+74+96+56}{10} \end{equation*} \\ \mu=\frac{733}{10}=73.3 \\ \mu=73.3 \\ \\ Cool \\ \begin{equation*} \mu=\frac{53+7+73+4+70+82+73+40+50+10}{10} \end{equation*} \\ \mu=\frac{462}{10}=46.2 \\ \mu=46.2 \end{gathered}[/tex]Median:
[tex]\begin{gathered} Warm \\ \text{Arrange data set in ascending order:} \\ 13,56,61,68,74,80,89,96,96,100 \\ Median=\frac{74+80}{2} \\ Median=\frac{154}{2}=77 \\ Median=77 \\ \\ Cool \\ \text{Arrange the data in ascending order:} \\ 4,7,10,40,50,53,70,73,73,80 \\ Median=\frac{50+53}{2} \\ Median=\frac{103}{2}=51.5 \\ Median=51.5 \end{gathered}[/tex]What would be the answer
Rational numbers are are fractions in which the numerator and denominator are integers. Looking at the given function,
- 2/3 + 1/5 = - 7/5
The numerator and denominator are integers. This is the only option that would give us a rational number
Thus, the correct option is
D. - 2/3