Rewrite in exponential form: log (Base v) 45 = u
Answer:
\(v^u=45\)Explanation:
Given the logarithm form of the expression:
\(\log _v45=u\)To write it in exponential form, the following applies:
0. The Base becomes the base of the index form.
,1. The number on the other side of the log operator becomes the index.
,2. The number whose log is being found is the answer.
Therefore, the exponential form is:
\(\begin{gathered} v^u=45 \\ v\text{ raised to the power of u = 45} \end{gathered}\)The diagram below is an illustration:
A line passes through (-3, -2) and is perpendicular to 3x - 2y = 7.
What is theFind the image of A(6, -4) after it is reflected over the line y = - 2, then reflected over the line x = 1.
(-4, -4)
(-4, 0)
(6, 2)
(-4, 6)
Choose values for A and B to create infinitely many solutions to this system of equations.
To create infinitely many solutions to this system of equations, select values for A and B. The given system of equations is as follows: 2x - 3y = A and 4x - 6y = B.The first equation can be obtained by multiplying the second equation by 1/2.
Therefore, any value of A and B that make this statement true will produce an infinite number of solutions. The two equations are the same thing; they differ only in their representation.Therefore, the answer is that we require to multiply the second equation by 1/2 in order to get the first equation. Any value of A and B that make this statement true will produce an infinite number of solutions. Let us first write the two equations that we have been given:2x - 3y = A (Equation 1)4x - 6y = B (Equation 2)
Now, let's analyze these equations one by one and find a way in which they are related to each other. As we can see, the second equation is exactly twice the first equation. Therefore, we can obtain the first equation by multiplying the second equation by 1/2:4x - 6y = B2x - 3y = (1/2)B Therefore, any value of A and B that make this statement true will produce an infinite number of solutions.
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What is the result of 54 х 18 written in standard form?
The length of a rectangle is five times its width.
If the area of the rectangle is 405cm^2, find perimeter
Answer:
108
Step-by-step explanation:
Let's say the width is x
Of the length is 5 times the width, then the length is 5x
Area = length * width
405 = x * 5x
405 = 5x^2
405/5 = 5x^2/5
81 = x^2
Take the square root of both sides
2/[81 = 2/[x^2
9 = x = width
9 × 5 = 45 = length
Perimeter = 2 × length + 2 × width
2 × 45 + 2 × 9
90 + 18 = 108
1. A scientist is growing cell cultures and examining the effects of various substances on them as part of his research. The culture in one petri dish increases according to the expression +47 + 4 for timet in minutes. Another increases according to 12 + 2t+4. He needs to feed all the cells equally, so he needs to know the expression for the total number of cells in both dishes because the food is proportional to the total number of cells. Find the expression.
Pay attention in class
The dashed triangle is the image of the solid triangle for a dilation with center at the origin. What is the scale factor?
The scale factor using in that dilation of the dashed triangle would be = 3:1
What is a scale factor?A scale factor is defined as the ratio that exists between an original size of an object and the new formed size of the same object.
The formula that can be used to calculate the scale factor ;
Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
Using the base of the triangle from the centre of origin in the graph;
The dimension of the new shape = 18
The dimension of the original shape = 6
scale factor = 18/6 =3
That is, the scale factor = 3:1
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A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t2 + 40t + 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0.2 s and 2.7 s. Which solution can be eliminated and why?
A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t² + 40t + 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0.2 s and 2.7 s.
the solution to be eliminated is -0.2s this is because time do not have negative values
What is a quadratic equation?ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a.
It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be real or complex.
Considering the given function, the answer is both real one is negative the other is positive.
The solution in this case represents time, and time of negative value do not apply in real life
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as in example 2.38, assume that 90% of the coins in circulation are fair, and the remaining 10% are biased coins that give tails with probability 3/5. i hold a randomly chosen coin and begin to flip it. (a) after one flip that results in tails, what is the probability that the coin i hold is a biased coin? after two flips that both give tails? after n flips that all come out tails? (b) after how many straight tails can we say that with 90% probability the coin i hold is biased? (c) after n straight tails, what is the probability that the next flip is also tails? (d) suppose we have flipped a very large number of times (think number of flips n tending to infinity), and each time gotten tails. what are the chances that the next flip again yields tails?
The probability that the coin is a biased coin after one flip that results in tails is about 10.9%.
Bayes' theorem is a mathematical formula that helps us update our beliefs about the probability of an event occurring based on new information or evidence. It involves the prior probability, which is our initial belief about the probability of an event, and the likelihood of the evidence given that the event has occurred. By combining these two pieces of information, Bayes' theorem allows us to calculate the updated or posterior probability of the event occurring.
After one flip that results in tails, the probability that the coin is a biased coin can be found using Bayes' theorem:
P(biased coin | tails) = P(tails | biased coin) * P(biased coin) / P(tails)
P(tails | biased coin) = 3/5 (given)
P(biased coin) = 0.1 (given)
P(tails) = P(tails | fair coin) * P(fair coin) + P(tails | biased coin) * P(biased coin)
= 1/2 * 0.9 + 3/5 * 0.1
= 0.55
Therefore,
P(biased coin | tails) = (3/5 * 0.1) / 0.55
= 0.109 (approximately)
Thus, the probability that the coin is a biased coin after one flip that results in tails is about 10.9%.
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Assume that 90% of the coins in circulation are fair, and the remaining 10% are biased coins that give tails with probability 3/5. i hold a randomly chosen coin and begin to flip it.
(a) after one flip that results in tails, what is the probability that the coin i hold is a biased coin? after two flips that both give tails? after n flips that all come out tails?
When you
divide a whole number by a unit fraction
explain how you can find the quotient
14. Higher Order
To find the quotient of whole number divided by a unit fraction the steps are discussed below.
We have to divide a whole number by a unit fraction.
let the whole number be 10 and fraction is 1/2.
So, division is
= 10 / (1/2)
Now, Reciprocate the fraction in the denominator as
= 10 x 2/1
= 20
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Given:
b (x) = x2+7x
Find
B(7)
Answer:
Step-by-step explanation:
b(7) = 7^2 + 7(7)
B(7) = 49 + 49
B(7) = 98
What are the 4 tests for similar triangles?
The 4 tests for similar triangles are:-
AAA: Three pairs of equal angles.
SSS: Three pairs of sides in the same ratio.
SAS: Two pairs of sides in the same ratio and an equal included angle.
ASA: Two angles and the side included between the angles of one triangle are equal
What is AAA,SAS,ASA,SSS?
According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle.
According to the SAS rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle.
According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle.
According to the AAA rule, "if in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion), and hence the two triangles are identical."
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A circle graph has four sections. One section makes up 45% of this circle graph. Determine the central angle measurement. Question 2 options: 162° 16,200° 8° 360°
The central angle measurement of the section that makes up 45% of the circle graph is 162 degrees. Answer: 162°
What is a circle?It is the center of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
According to the given information:If one section makes up 45% of the circle graph, then the other three sections combined make up the remaining 55% of the graph. Since the circle graph represents a full circle, which has a total central angle measurement of 360 degrees, we can set up the following proportion:
45/100 = x/360
where x is the central angle measurement of the section that makes up 45% of the graph. To solve for x, we can cross-multiply and simplify:
45 * 360 = 100 * x
x = 16,200/100
x = 162
Therefore, the central angle measurement of the section that makes up 45% of the circle graph is 162 degrees. Answer: 162°
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Let F(x)=f(f(x)) and G(x)=(F(x)) 2 and suppose that f(8)=14,f(14)=3,f(14)=15,f(8)=10 Find F(8) and G(8) F(8)=
G(8)=
The value of F(8) is 3 and G(8) is 9. Given the function f(x) and specific values for f(8), f(14), and f(15), we can find F(8) and G(8).
To find F(8), we substitute x = 8 into the function F(x) = f(f(x)). Since f(8) = 14, we replace f(x) in F(x) with 14:
F(8) = f(f(8)) = f(14)
Similarly, to find G(8), we substitute x = 8 into the function G(x) = (F(x))^2. Since we need to find F(8) first, we can substitute the value of F(8) into G(x):
\(G(8) = (F(8))^2\)
Now, let's calculate F(8) and G(8) using the given values of f(8), f(14), and f(15). According to the information provided, f(8) = 14, f(14) = 3, and f(15) = 15.
To find F(8), we substitute f(8) = 14 into f(f(x)):
F(8) = f(f(8)) = f(14) = 3
Therefore, F(8) is equal to 3.
Now, let's find G(8) by substituting F(8) = 3 into G(x):
\(G(8) = (F(8))^2 = (3)^2 = 9\)
Therefore, G(8) is equal to 9.
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in the example on page 26, if linda had started with one yard of fabric and used 5 8 of a yard, how much fabric would be left?
The statement that is true is:
Statements 1 and 3
Let's examine each statement individually:
If n is a multiple of 8, then n is a multiple of 4. This statement is true because every number that is divisible by 8 is also divisible by 4. Since 8 is a multiple of 4, any multiple of 8 will have factors of both 8 and 4. If n is a multiple of 18, then n is a multiple of 2.
This statement is also true. Any number that is divisible by 18 is also divisible by 2 because 18 contains a factor of 2. Every multiple of 18 will have at least one factor of 2.
Statement 2 is not true. If n is a multiple of 18, then n is a multiple of 9.
This statement is false because there are numbers that are multiples of 18 but not multiples of 9. For example, 18 itself is a multiple of 18 but not a multiple of 9, as 18 divided by 9 is equal to 2.
Therefore, the correct answer is c) Statements 1 and 3.
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the rescue center currently has 9 snow geese each goose gets 16 oz of seed's there is 1,656 seeds in all how many days of food until the shelter runs out
Answer:
A soultion is provided that makes assumptions about missing information.
Step-by-step explanation:
The statement ". . . each goose gets 16 oz . . ." is missing some information about a time frame. Is it 16 oz per day, week, month? The question cannot be answered without this information.
We also don't know the relationship between the number of seeds and ounces. Is 16 oz 1 seed, 10 seeds, 1000 seeds? Again, we cannot solve this without additional information.
To add some insight how to solve the problem, lets make two assumptions:
Assume 16 oz/week. We can write this as a conversion factor: (16 oz food)/(1 snow goose).
Assume 10 seeds/oz.
The Rescue Center has 1,656 seeds in total.
(1,656 seeds)
Each snow goose gets 16 oz of seeds a week. That is (16 oz)*(10 seeds/oz) = 160 seeds/week per goose.
There are 9 geese, so they consume (9 geese)*(160 seeds/week/goose) = 1440 seeds/week
There are 1,656 seeds. At 1,440 seeds/week, they will last (1,656 seeds)/(1,440 seeds/week) = 1.15 weeks.
PLEASE HELP WILL GIVE BRAINLIST IF CORREC IT'S DUE IN 3MIN
The scores earned in a flower-growing competition are represented in the stem-and-leaf plot.
2 0, 1, 3, 5, 7
3 2, 5, 7, 9
4
5 1
6 5
Key: 2|7 means 27
What is the appropriate measure of variability for the data shown, and what is its value?
The IQR is the best measure of variability, and it equals 16.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 16.
the answer to your math question is "The IQR is the best measure of variability, and it equals 16".
Evaluate the expression 3x2t when t is 1
Hey there!
The answer to your question is 6.
To solve this equation when t = 1, we can simply plug t into the equation.
3 x 2(1)
3 x 2
5
Hope this helps your assignment! Have a great day! Good luck!
You put $1500 into an account that earns 4% interest. How much will be in the account after 6 years if the account is compounded monthly?
Answer:
hence ,
answer is R.s 360
Step-by-step explanation:
I=PTR/100
=1500×6×4/100
=360
jackie wants to learn more about local college. which of the following is a statistical question jackie could ask?
A. does the collage have art classes
B. what is the address of the college
C. how old are the student's
D. does the collage have a women's soccer team
Find the equation of the straight line which makes a negative intercept of 4 units on the x - axis and passes through the point (2‚ 3).
Answer:
y = 1/2x + 2.
Step-by-step explanation:
It passes through the points (-4, 0) and (2,3) so
the slope (m) = (3-0)/(2-(-4)) = 3/2 = 1/2.
Using the point slope form of a straight line:
y - y1 = m(x - x1):
y - 3 = 1/2(x - 2)
y = 1/2x - 1 + 3
y = 1/2x + 2 is the required equation.
Use power series to solve the equation y ′′
+y=0.
To solve the given equation \($y''+y=0$\) using power series, we can assume that y can be written as the sum of an infinite power series of the form:$y = \sum_{n=0}^{\infty}a_nx^n$Taking the first and second derivatives of this series expansion,
\(we get:$y' = \sum_{n=1}^{\infty}na_nx^{n-1}$and $y'' = \sum_{n=2}^{\infty}n(n-1)a_nx^{n-2}$\)
Substituting these expressions into the given equation, we get:$$\(\sum_{n=2}^{\infty}n(n-1)a_nx^{n-2}+\sum_{n=0}^{\infty}a_nx^n=0\)$$Simplifying the above equation:$$\sum_{n=0}^{\infty}(n+2)(n+1)a_{n+2}x^n+\sum_{n=0}^{\infty}a_nx^n=0$$Now,
let's consider the power of $x^n$ in this equation. We get:$(n+2)(n+1)a_{n+2}+a_n=0$Hence, the recursive formula for the coefficients of the power series is:$a_{n+2}=-\frac{a_n}{(n+2)(n+1)}$We also have the initial conditions:$a_0=y(0)$ and $a_1=y'(0)$Using these, we can find the coefficients of the power series one by one, starting with $a_0$ and $a_1$. Then, using the recursive formula,
we can find all the other coefficients.In conclusion, we have solved the given differential equation $y''+y=0$ using power series. The power series solution is given by:$y = a_0+a_1x-\frac{1}{2!}a_0x^2-\frac{1}{3!}a_1x^3+\frac{1}{4!}a_0x^4+\frac{1}{5!}a_1x^5-\cdots$Note that this series is an alternating series, with every other term having a negative coefficient.
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What are the numerical measures of each angle in the diagram? 1 and 3 measure degrees. 2 and 4 measure degrees. (3x - 1)º (2x + 9)°
Answer:
Step-by-step explanation:
In the diagram shown, the measure of angle 1 is oppositely directed to angle 2 and oppositely directed angles are equal.
Hence <1 = <3
Given < 1 = 3x-1 and <3 = 2x+9
Hence 3x-1 = 2x+9
collect like terms
3x-2x = 9+1
x = 10°
Since <1 = 3x-1
on substituting x = 10
<1 = 3(10)-1
<1 = 30-1
<1 = 29°
<1+<2 = 180 (angle on a straight line)
29+<2 = 180
<2 = 180-29
<2 = 151°
Similarly, on substituting x = 10 into <3
<3 = 2x+9
<3 = 2(10)+9
<3 = 20+9
<3 = 29°
<3+<4 = 180 (angle on a straight line)
29+<4 = 180
<4 = 180-29
<4 = 151°
Answer:
keeping it simple answers are 29 and 151 now thats simple
Step-by-step explanation:
At the carnival, the ratio of people who won the ring toss game to lost it was 8:5. If 24
people won, how many people would have lost?
Answer:
if 24 people won, 15 people lost
Use the reference angle to find the exact value of each expression. Do not use a calculator. a) cos210°
b) cos600°
c) sin(−240°)
The exact values are a) cos210° = -√3/2, b) cos600° = 1/2, c) sin(-240°) = -√3/2.
To find the exact values of the expressions without using a calculator, we can use the reference angle and the unit circle.
a) For cos210°, we can use the reference angle of 30° in the third quadrant. In the third quadrant, the cosine function is negative. Therefore, cos210° = -cos30° = -√3/2.
b) For cos600°, we can find the coterminal angle within one revolution by subtracting 360° multiple times until we get an angle between 0° and 360°. The coterminal angle of 600° is 600° - 360° = 240°. In the unit circle, the cosine of 240° is positive. Therefore, cos600° = cos240° = 1/2.
c) For sin(-240°), we can find the coterminal angle within one revolution by adding 360° multiple times until we get an angle between 0° and 360°. The coterminal angle of -240° is -240° + 360° = 120°. In the unit circle, the sine of 120° is negative. Therefore, sin(-240°) = -sin120° = -√3/2.
Therefore, the exact values are: a) cos210° = -√3/2, b) cos600° = 1/2, c) sin(-240°) = -√3/2.
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Robert is running a race to raise money for cancer research. He raised $5 for the first mile
he runs, $6 for the second mile, and $7.20 for the third mile.
If this pattern continues, what is the total amount of money he will raise if his race is
26 miles total?
The pattern tells that the amount raised by Robert in 26th mile is $90.
What is a pattern?
A recurring arrangement of numbers, forms, colours, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern.
The amount of money raised by Robert for first mile = $5
The amount of money raised by Robert for second mile = $6
The amount of money raised by Robert for third mile = $7.2
The difference between amount raised in first and second mile = $1
The difference between amount raised in second and third mile = $1.2
Similarly, the difference between amount raised in third and fourth mile will be = $1.4
Similarly, the difference between amount raised in fourth and fifth mile will be = $1.8
Following this pattern the difference between 25th and 26th mile will be = (26 × 0.2) + 0.4 = $5.8
Now, the amount raised in 26th mile = 84.2 + 5.8 = 90
Therefore, the amount raised is $90.
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What is the y-intercept of the function f(x) = -2/-9x+1/3?
Answer:
b = 1/3
Step-by-step explanation:
The general structure of equations in slope-intercept form is:
y = mx + b
In this form, "m" represents the slope and "b" represents the y-intercept.
The given equation is already in slope-intercept form. In other words, you have already been given "m" and "b". Therefore, the value which corresponds with the y-intercept is (1/3).
f(x) = mx + b
f(x) = -(2/9)x + 1/3
yeah please help me
Answer:
Its B and E
Step-by-step explanation:
PLS MAKE ME BRAINLIEST
A grocery store chain introduces a new brand of cereal in several of its stores. The function B(w)=120w150+w2 for w≥0 models the number of boxes, B, in thousands, of the cereal sold after w weeks. The graph of this function is shown below.
Select the THREE true statements regarding the graph of B(w).
A
Based on the zeros of the function, the number of boxes of cereal sold is 0 after 0 weeks.
B
Based on the zeros of the function, the number of boxes of cereal sold is 0 after 1,250 weeks.
C
Based on the end behavior of the function, the number of boxes of cereal sold will keep falling after reaching the maximum.
D
Based on the asymptote of the function, the number of boxes of cereal sold will never fall below 800 after reaching the maximum.
E
Based on the asymptote of the function, the number of boxes of cereal sold will never reach 0 after the cereal is introduced in the store.
The THREE true statements regarding the graph of B(w) are;
A) Based on the zeros of the function, the number of boxes of cereal sold is 0 after 0 weeks.
C) Based on the end behavior of the function, the number of boxes of cereal sold will keep falling after reaching the maximum.
E) Based on the asymptote of the function, the number of boxes of cereal sold will never reach 0 after the cereal is introduced in the store.
How to Interpret Quadratic Graph?
We are given the graph represented by the quadratic function;
B(w) = 120w/(150 + w²) for w ≥ 0 that models;
the number of boxes, B, in thousands, of the cereal sold after w weeks
From the graph, we can see that at the origin which is the coordinate (0, 0) that it remains so and as such the number of boxes of cereal sold is 0 after 0 weeks. Thus, option A is correct
Secondly, from the given graph, we see that the graph starts rising from zero to a maximum after which it keeps falling. Thus, we can say that option C is correct
Lastly, we see that the graph asymptote approaches 500 thousand boxes but never gets to zero and as such we can say that option E is correct.
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The area of the trapezium above is 22 cm².
What is the value of x ?
Answer:
4cm
Step-by-step explanation:
Given area= 22cm²
Height =4cm
Parallel sides = xcm and 7cm
Area of trapezium = ½( sum of parallel sides) x height
22cm² = ½(xcm+7cm)×4cm
22cm²= ½ ( x+7)cm x 4cm
opening the bracket
22cm²= 4x+28/ 2
cross multiply
44cm²=4x+28
4x=44-28
4x=16
x=4cm