Answer:
Step-by-step explanation:
In algebraic expressions that use variables (written as letters), you can write them directly after a normal number, with no symbol between them.
...
Use a ⋅ or × sign if you see words like double, per, or product.
Twice 16 → 2 ⋅ 16.
Five per day → 5 ⋅ d or 5d. ...
The product of 8 and 20 → 8 ⋅ 20.
Use the standard normal distribution to find the probability P(z < –2.08)
P(z < -2.08) = 0.018763
Explanations:From the standard normal distribution table, we can check the probability given any z-score
Therefore, checking P(z < -2.08) from the standard normal distribution:
P(z < -2.08) = 0.018763
A model for the potential through the heart (between sinoatrial node and atrioventricular node) for an individual is…. Where P(v) is the new voltage (in millivolts) after 1 second given a previous voltage v and u is a positive constant called the updating potential. A. Calculate, including units, the value of P(100): ______ mV B. Find the average rate of change in P on the interval [30, 120] (the answer will contain u). = __________ D. The system is said to be in equilibrium at a value for v for which P(v) = v. For what range of values or u does this system have an equilibrium? (Use interval notation) __________
The model is given in the question.
a. The value of P(100) is
[tex]P(100)=0.7\times100=70mV[/tex]b. The average rate of change in P on the interval [30,120] is
[tex]A=\frac{P(120)-P(30)}{120-30}=\frac{0.7\times120-(0.7\times30+u)}{90}[/tex][tex]A=\frac{84-21-u}{90}=\frac{63-u}{90}[/tex]c. The graph of P (v) is represented the linear function.
Yes it represents a linear function.
A rabbit runs 35 miles per hour. A fox can run 21 miles in half an hour. Which animal is faster, and by how much?
Answer:
The fox can run faster by a factor of 7 miles per hour
Step-by-step explanation:
If the fox runs 21 miles in half of an hour, that means that by multiplying the fraction 21miles/0.5hours by 2/2 you can find that the fox runs 42 miles per hour, 7 miles per hour faster than the rabbit.
Answer:
The Fox, by 7 Miles per hour
Step-by-step explanation:
The rabbit runs 35 Miles per hour
The Fox runs 21 in half an hour
1 hour - 30 minutes = 30 minutes meaning we have to double the foxes miles
21 x 2 = 42
42>32
To find out by how much do 42-32 and we get 7 Miles per hour.
Solve: (2,1); m=undefined. Answer has to be in slope intercept form, so y=mx+b. SHOW ALL WORK SO I CAN HAVE A BETTER UNDERSTANDING :)
Answer:
x = 2
Step-by-step explanation:
So this seems kind of a trick question. This is why. The given slope is undefined. That means this is a vertical line. Vertical lines cannot be written in slope-intercept form,
y = mx+b.
Vertical lines have the equation "x = anumber" It literally cannot be written in the form y=mx+b.
The point given is (2,1) this is in the form (x,y) so x is 2 and y is 1. We are interested in the x.
x is 2 is written as:
x = 2 This is the equation of the lines through (2,1) with m=undefined.
4x3 − 6x2 − 28x Is this a special product?
ANSWER:
It is not a special product
STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]4x^3-6x^2-28x[/tex]Among the special products we have:
The sum and difference of same terms
The square of a binomial
The cube of a binomial
Let's factor the expression to determine if it satisfies any of the above:
[tex]\begin{gathered} 2x\cdot\left(2x^2-3x-14\right? \\ 2x^{2}-3x-14 \\ -3x=4x-7x \\ 2x^2+4x-7x-14 \\ 2x\left(x+2\right?-7\left(x+2\right? \\ 2x\cdot\left(x+2\right)\cdot\left(2x-7\right) \end{gathered}[/tex]Therefore, we can determine that it does not belong to the group of special products.
A dinner plate has 25.12 inches of metal around it's edge. What is the radius of the plate?
Assuming your teacher wants you to use 3.14 for pi, then,
C = circumference = perimeter around the circle
C = 2*pi*r
r = C/(2*pi)
r = (25.12)/(2*3.14)
r = 4 inches is the radius
The radius of the circle is 4 inches
What is a Circle?
A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the centre for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
Given data ,
Let the circumference of the circle be = A
Now , Circumference A = 25.12 inches
The circumference of circle = 2πr
π = 3.14
Substituting the values in the equation , we get
2πr = 25.12
Divide by π on both sides , we get
2r = 8
Divide by 2 on both sides , we get
r = 4 inches
Therefore , the value of r is 4 inches
Hence , The radius of the circle is 4 inches
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Part 2: Multiple Choice Must show all work to get full credit.
The correct value of x is -6, as determined by the equation KL + LM = KM. As a result, Option C is correct.
What is an equation and what type is it?Equations are classified into two types: identities and conditional equations. An identity holds true for all variable values. A conditional equation is only true for specific variable values. An equation is formed by joining two expressions with an equals sign ("=").From the given figure,
KL + LM = KM
15 + 2x + 10 = x + 19
2x + 25 = x + 19
x = -6
Therefore, the correct value of x is -6 which is obtained from the given equation KL + LM = KM. So, Option C is correct.
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Greg graduated in the bottom 9% of his class. If the mean was 585 and the standard deviation was 134, and the distribution was normal, what was Greg's raw score?
Greg's raw score in the test is 405
How to determine the raw score of the test?The given parameters are
Mean = 585Standard deviation = 134Proportion, p = bottom 9%The above implies that
z = P(p < 0.09)
From z tables of probabilities, we have
z = -1.34
The z-score of the data value is calculated using the following formula
z = (raw score - mean value)/standard deviation
Substitute the given parameters in the above equation
-1.34 = (raw score - 585)/134
This gives
-180 = raw score - 585
So, we have
raw score = 585 - 180
Evaluate
raw score = 405
Hence, the raw score is 405
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Graph the solution set l 2x + 4l + 2 <= 8
ANSWER :
EXPLANATION :
From the problem, we have :
[tex]\begin{gathered} \lvert{2x+4}\rvert+2\le8 \\ \text{ which can be simplified as :} \\ \lvert{2x+4}\rvert\le6 \end{gathered}[/tex]Note that in solving absolute values, the terms inside the absolute value sign can have inverse signs.
Case 1 : Positive
[tex]\begin{gathered} 2x+4\le6 \\ 2x\le2 \\ x\le\frac{2}{2} \\ \\ x\le1 \end{gathered}[/tex]Case 2 : Negative, the symbol will change since we are multiplying a negative number
[tex]\begin{gathered} -(2x+4)\ge6 \\ -2x-4\ge6 \\ -2x\ge10 \\ x\ge\frac{10}{-2} \\ \\ x\ge-5 \end{gathered}[/tex]So the solution is :
[tex]\begin{gathered} x\le1\quad and\quad x\ge-5 \\ \text{ when written together :} \\ -5\le x\le1 \end{gathered}[/tex]or in interval notation :
[-5, 1]
The graph of it will be :
multiple fractions (reduce to lowest terms or tenths)61/2×41/4
Answer:
312.6
Explanation:
Given the expression
61/2 * 41/4
Multiply both numerator and denominator
= 61/2 * 41/4
= (61*41)/(2*4)
= 2501/8
= 312.625
To nearest tenth 61/2 * 41/4 = 312.6
help pleaseeee. I need it quick
x: -3 -2 -1 0 1 2 3 4
y: 6 0 -4 -6 -6 -4 0 6
You plug in x into the equation and you get the value of y. Then graph the points: (-3, 6) (-2, 0) (-1, -4) (0, -6) (1, -6) (2, -4) (3, 0) (4, 6).
Hope it helps! :D
Help mee pleasee!!
thank you <3
The linear equation y = -500x + 5000 models the price-sales relationship for the toy and the daily sales of the toy would be $1250 if the price is set at $7.50.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The line must pass through points (6, 2000) and (8,1000) which is given in the question.
We have to determine the slope of the line :
m = (y₂ - y₁)/(x₂ -x₁ )
m = (1000 - 2000)/(8 - 6)
m = -1000/2
m = -500
This represents new assistants per year
So with through points (6, 2000) and (8,1000), the equation becomes
y - 2000 = -500(x -6)
y = -500x + 3000 + 2000
y = -500x + 5000
Using this equation to predict the daily sales of the toy if the price is set at $7.50.
Assume that the ratio of change in price to change in daily sales is constant and let x be the price of the toy and y be the number of sales.
Substitute the value of x = 7.50
y = -500(7.50) + 5000
y = -56000 + 294000
y = 1250
Hence, the daily sales of the toy would be $1250 if the price is set at $7.50.
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PointProduction chocolate barsProduction cans of colaA 0 100B 10 90C 20 70D 30 40E 40 0The above table shows production points on Sweet-Tooth Land's production possibilities frontier. Which of the following statements is TRUE?A.Producing 0 chocolate bars and 100 cans of cola is both attainable and efficient.B.Producing 20 chocolate bars and 80 cans of cola is attainable but inefficientC.Producing 30 chocolate bars and 38 cans of cola is both attainable, with an inefficientD.Producing 40 chocolate bars and 0 cans of cola is both attainable and inefficient
First look and see if each of the values are true (attainable) before looking at efficiency
A.Producing 0 chocolate bars and 100 cans of cola is both attainable and efficient.
This is attainable
B.Producing 20 chocolate bars and 80 cans of cola is attainable but inefficient
This is not attainable
C.Producing 30 chocolate bars and 38 cans of cola is both attainable, with an inefficient
This is attainable
D.Producing 40 chocolate bars and 0 cans of cola is both attainable and inefficient
This is attainable
Now lets looks at efficiency
efficient when it is producing at the lowest point on the graph
Inefficient is below the graph
D should be efficient
A should be efficient
I am not sure why C is wrong
Construct an appropriate triangle to find the missing values
This can be solved using trigonometry.
What is trigonometry?
Trigonometry is a field of mathematics that examines correlations between triangle side lengths and angles (from the Ancient Greek words "trigonon" and "metron"). The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research. While Indian mathematicians produced the earliest tables of values for trigonometric ratios (also known as trigonometric functions), such as sine, the Greeks concentrated on chord computation. Trigonometry has been used historically in fields including geodesy, surveying, celestial mechanics, and navigation. Trigonometry has a wide variety of identities. In order to simplify an expression, identify a more practical version of an expression, or solve an equation, trigonometric similarities are frequently employed to rewrite trigonometrical statements.
Using trigonometric relations,
cos 30° = cos π/6 rad = √3/2
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Health and Fitness Masha is training for a marathon. She is doing
tempo runs to increase her speed. In tempo runs, a runner varies
their pace during the run. Masha jogs 1 mile, then runs at a fast pace
for 11 miles. She finishes by walking 2 miles to cool down. Write a
numerical expression to model the number of miles Masha runs,
walks, or jogs.
The numerical expression to model the number of miles Masha runs, walks, or jogs is 14.
What is meant by numerical expression?Mathematical operations like addition, subtraction, multiplication, and division can be used to mix integers and numbers to create a numerical expression.
The rule should state something along the lines of: "When simplifying, parentheses must be simplified first, followed by all exponents, all multiplication, and ultimately, all addition."
Based on the given conditions, formulate: 2 + 1 + 11
Calculate the sum or difference: 3 + 11
Calculate the sum or difference: 14
Therefore, the numerical expression to model the number of miles Masha runs, walks, or jogs is 14.
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on a certain hot summer day 629 people use the public swimming pool The daily prices are $1.25 for children and $2.50 for adults The receptionist for admission totaled $1,200 how many children and how many adults swim at the public pool that day
Let the number of children be "c" and the number of adults be "a".
There are a total of 629 adults and children.
Thus, we can write an equation:
[tex]c+a=629[/tex]Price of each children admit is 1.25 and each child admit is 2.50 for a total of $1200.
Thus, we can write an equation to represent this information as:
[tex]1.25c+2.50a=1200[/tex]We can solve the system of 2 equations we got and find out the values of "a" and "c".
Solving the first equation for c:
[tex]\begin{gathered} c+a=629 \\ c=629-a \end{gathered}[/tex]We substitute it into second equation and figure out a:
[tex]\begin{gathered} 1.25c+2.50a=1200 \\ 1.25(629-a)+2.50a=1200 \\ 786.25-1.25a+2.50a=1200 \\ 1.25a=1200-768.25 \\ 1.25a=413.75 \\ a=\frac{413.75}{1.25} \\ a=331 \end{gathered}[/tex]Now, we simply find out c:
[tex]\begin{gathered} c=629-a \\ c=629-331 \\ c=298 \end{gathered}[/tex]Answer:
Children = 298Adults = 331help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
its 5
Step-by-step explanation:
f
dddd
Studying for a test, need some help solving this question
Solution
Part A
To find C
[tex]_{\angle\text{ C+}\angle A+\angle B=180^0(Sum\text{ of angles in a triangle\rparen}}[/tex][tex]\begin{gathered} \angle C+33.84+19.32=180 \\ \angle C+53.16=180 \\ \angle C=180-53.16 \\ \angle C=126.84^0 \\ \end{gathered}[/tex]Part B
To find a
Using sine rule
[tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex][tex]\begin{gathered} \frac{sin33.84}{a}=\frac{sin126.84}{13.95} \\ cross\text{ multiply} \\ asin126.84=13.95sin33.84 \\ divide\text{ both side by sin126.84} \\ \\ a=9.70672 \end{gathered}[/tex]Part C
To find b
Using sine rule
[tex]\begin{gathered} \frac{sin33.84}{9.70672}=\frac{sin19.32}{b} \\ \\ \\ b=5.76683 \end{gathered}[/tex]Greg Losier put $26,500 down on a $92,500 home.
How much did he have to mortgage?
Using mathematical operations we conclude that Greg has to mortgage the amount of $66,000.
What are mathematical operations?An operation, also known as an "operand" or "argument," is a function in mathematics that converts zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands.Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the operations that are most frequently studied. The addition, subtraction, multiplication, division, exponentiation, and modulus operations are carried out by the arithmetic operators.So, the mortgage will be:
$92,500 - $26,500Solve this expression as follows:
$92,500 - $26,500$66,000Therefore, using mathematical operations we conclude that Greg has to mortgage the amount of $66,000.
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Helen borrowed $2,500 for home repairs. She paid back 24 payments of$115 each. How much did she pay in interest on the loan?a. $108.96b. $4.79c. $2,760d. $260
To solve this problem, we will compute the total amount Helen paid back and we will subtract $2,500 from it.
To determine the total amount she paid back we multiply the number of payments by the amount of each payment:
[tex]T=24\times115\text{dollars}=2760\text{ dollars.}[/tex]Subtracting $2,500 from the above result we get:
[tex]2760-2500=260\text{dollars.}[/tex]Answer: Option d.
Figure W was ___ to create W’. Figure W’ was dia lates by a scale factor of ___ fromThe origin to create w”
Transformations
One of the rigid transformations is reflection. When a figure is reflected across some line, it maps to the very same shape but inverted as if the line was a mirror.
Right between figures W and W' the y-axis separates two identical images as if the y-axis was a mirror, thus:
Figure W was reflected over the y-axis to create figure W'
A Dilation from the origin maps an object to another such that its vertices are all multiplied by a common factor (scale factor).
For example, the upper-right vertex of W' is located at (2-2). The upper-right vertex of W'' is at (4,-4). The scale factor is 2.
The bottom-left vertex of W' is at (4,-4) and the bottom-left vertex of W'' is at (8,-8). We find the same scale factor of 2. If we tested all of the vertices, we'll obtain the same scale factor of 2, thus:
Figure W' was dilated by a scale factor of 2 from the origin to create figure W''
5÷4=
what is the quotient
Elsie has just finished polishing some of her antique penny collection. She has twelve pennies, each with a different date. To store her coins she has purchased many plain black bags, and wishes to put the same number of coins in each bag. She has no restriction on the number of bags she can use. In how many possible ways can she store her coins
The possible ways Elsie (combinations) can store her 12 coins in the bags she purchased is 6 ways
What is a combination in mathematics?A combination is the number of possible arrangements.
The number of coins = 12 coins
The number of black bags = Many
Number of coins per bag = The same number of coins
Required;
The number of ways Elsie can store her coins
Solution;
The ways the coins can be stored is given by the factors of 12 which are; 1, 2, 3, 4, 6, and 12
The coins can therefore be stored as follows;
1 coin per bag to give 1 × 12 = 12 bags of coins2 coins per bag to give 12 ÷ 2 = 6 bagsShared into 3 coins each to give 12 ÷ 3 = 4 bags 4 coins to give 12 ÷ 4 = 3 bags6 coins each to give 12 ÷ 6 = 2 bags12 coins in each bag to give 12 ÷ 1 = 1 bagsThe possible number of ways Elsie can store the coins is 6 ways
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1:
Jerrod brought 48 cupcakes to school. At school, he gave 3 cupcakes to
each student in his class. He has 6 cupcakes remaining. How many
students are in Jerrod's class? Variable,equation and answer
Answer:
There were eight studentsin jerrods class
What is the greatest common factor of this expression?
12m + 18m2
A.
2m
B.
6m
C.
6
D.
2
Answer:
I think the answer is B because when you check the factors, you get 6 then you add your unit
Find the lateral area of a right cylinder with a diameter of 6.4 yards and a height of 16.2 yards. Round to the nearest tenth.
You can use the following formula in order to calculate the Lateral area of the right cylinder given in the exercise:
[tex]LA=2\pi rh[/tex]Where "LA" is the lateral area of the cylinder, "r" is the radius and "h" is the height.
In this case you know that its diameter is:
[tex]d=6.4yd[/tex]Since the diameter of a circle is twice the radius:
[tex]2r=6.4yd[/tex]Knowing that the height of the cylinder is:
[tex]h=16.2yd[/tex]You can substitute values into the formula and then evaluate, in order to find the lateral area:
[tex]\begin{gathered} LA=\pi(6.4yd)(16.2yd) \\ LA\approx325.7yd^2 \end{gathered}[/tex]Then, the answer is:
[tex]LA\approx325.7yd^2[/tex]step by step on how to solve -887.4 (-0.1) & -6 × 3.3
The numbers have opposite signs, so the result of the multiplication will be negative i.e -19.8.
We are given two mathematical expressions to be solved. An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms.
The first expression is solved below :
E1 = -887.4(-0.1)
We need to multiply the two numbers with each other. Both the numbers are negative, so the result of the multiplication will be positive.
E1 = 88.74
The second expression is solved below :
E2 = -6 × 3.3
This is a simple multiplication of two real numbers. The numbers have opposite signs, so the result of the multiplication will be negative.
E2 = -19.8
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Raymond places four colored blocks in a bag. The colors are red, blue, yellow and green. Without looking, he reaches into the bag andpulls one block out.What is the probability that the block he pulls out will be yellow?A. 1/4. B.1/3. C.3/1. D.4/1
Given:
Total number of colored blocks in the bag = 4
Given that Raymond picks one block out without looking(randomly), let's find the probability it is a yellow block.
Probablity can be said to be the likelihood of the occurence of an event.
Given:
Number of yellow blocks = 1
To find the probability that the blocks he pulls out will be a yellow block, apply the formula below:
[tex]P(\text{yellow)}=\frac{\text{Number of yellow blocks}}{Total\text{ number of blocks}}[/tex]Thus, we have:
[tex]P(\text{yellow)}=\frac{1}{4}[/tex]Therefore, the probability thatvthe block he pulls out will be yellow is ¼
ANSWER:
[tex]A\text{. }\frac{1}{4}[/tex]) Anita prepared 28 kilograms of
dough after working 4 hours. How
much dough did Anita prepare if she
worked for 5 hours? Solve using unit
rates.
Answer: should be around 35 kilos dont got an explaination just used meh brain
Step-by-step explanation:
Use the Factor Theorem to find the zeros of f(x) = x³+4x² - 4x - 16 given that (x - 2) is afactor of the polynomial.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given polynomial function
[tex]f(x)=x^3+4x^2-4x-16[/tex]STEP 2: Apply the factor theorem
A polynomial function f(x) has a factor (x-a) if and only if f(a) = 0, this means that (x-2) will be a factor if and only if f(2)=0.
By checking,
[tex]\begin{gathered} f(2)=2^3+4(2^2)-4(2)-16 \\ f(2)=8+16-8-16=0 \end{gathered}[/tex]Hence, (x-2) is a factor and the first zero is 2
STEP 3: We divide the polynomial by its factor to get the quotient expression
[tex]\frac{x^3+4x^2-4x-16}{(x-2)}=x^2+6x+8[/tex]STEP 4: we find out the factors of the quotient
If f(a) is zero, this means that a must be a factor of 16
The factors of 16 are 1,2,4,8,16
[tex]\begin{gathered} x^2+6x+8=(x+4)(x+2) \\ f(-4)=(-4^2)+6(-4)+8=16-24+8=0 \\ f(-2)=(-2)^2+6(-2)+8=4-12+8=0 \end{gathered}[/tex]Hence, (x+4) and (x+2) are also factors of the polynomial.
Therefore, the zeroes of the given function are:
[tex]2,-4,-2[/tex]