Answers
Given:
[tex]\frac{1}{2}+\frac{3}{4}[/tex]Let's add the fractions above.
To perform the addition, find the Lowest Common Multiple (LCM) of the denominators.
LCM of 2 and 4 = 4
Divide each denominator by the LCM and multiply the result with the numerator.
Thus, we have:
[tex]\begin{gathered} \frac{1}{2}+\frac{3}{4} \\ \\ \frac{2+3}{4}=\frac{5}{4} \\ \\ \frac{5}{4} \end{gathered}[/tex]Convert the improper fraction (5/4) to mixed fraction.
We have:
[tex]\frac{5}{4}=1\frac{1}{4}[/tex]ANSWER:
[tex]1\frac{1}{4}[/tex]Related Questions
Event A, Event B, and Event Care provided. Event A and Event B aremutually exclusive. Event A and Event C are not mutually exclusive.P(A) = 0.45P(B) = 0.30P(C) = 0.25What is the probability of the union of A and B?
Answers
Given data:
The probability of A is P(A)=0.45.
The probability of B is P(B)=0.30.
The expression for the mutually exclusive events is,
[tex]P(A\cap B)=0[/tex]The expression for the probability of A union B is,
[tex]\begin{gathered} P(A\cup B)=P(A)+P(B)-P(A\cap B) \\ =0.45+0.30-0 \\ =0.75 \end{gathered}[/tex]Thus, the probability of (AUB) is 0.75.
What's the divisor, dividend, Quotient, and reminder in a long divison problem
Answers
In a long division problem, say 8/5:
[tex]\frac{8}{5}\text{ is the quotient}[/tex]• 8 is the divisor
,• 5 is the dividend
[tex]\frac{8}{5}=1\frac{3}{5}[/tex]• 3 is the remainder.
Convert the numeral in base ten. (Explanation please)
Answers
Converting the given expression which is [tex]43_{8}[/tex] to base ten gives 35 in base ten.
How to convert a number in base eight to base tenConversion of bases is achieved based on how the conversion to be done are are basically of two methods which are
conversion from other bases to base tenconversion from base ten to other basesThe question is about converting other bases (base eight) to base ten. The steps required are as follows:
For other bases, the number 8 as used is replaced by the number required to be convertedThe exponents starts from zero and increases from left to right as seen belowThe given data is a number in base eight
[tex]43_{eight}[/tex]
[tex]43_{eight}=4*8^{1}+3*8^0[/tex]
[tex]43_{eight}=4*8+3*1[/tex]
[tex]43_{eight}=32+3[/tex]
[tex]43_{eight}=35[/tex]
The number 35 is now in base ten and can be written as [tex]35_{10}[/tex]
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determine the domain and range of the piecewise function graphed below
Answers
The domain is all the possible input values, and the range is all the possible output values.
So according to this function (Given in the question).
The domain is [-3, 5] and the range is [-5, 4]
That is all to this question.
currently, Yamir is twice as old as pato. in three years, the sum of their ages will be 30. if pathos current age is represented by a, what equation correctly solves for a?
Answers
The given situation can be written in an algebraic way.
If pathos age is a, and Yamir age is b. You have:
Yamir is twice as old as pato:
b = 2a
in three years, the sum of their ages will be 30:
(b + 3) + (a + 3) = 30
replace the b = 2a into the last equation, and solve for a, just as follow:
2a + 3 + a + 3 = 30 simplify like terms left side
3a + 6 = 30 subtract 6 both sides
3a = 30 - 6
3a = 24 divide by 3 both sides
a = 24/3
a = 8
Hence, the age of Pato is 8 years old.
Given that A = {1, 2,2 3} and B = {4, 6}, then find B×A
Answers
The solution for set B × A is {(4, 1), (4, 2), (4, 3), (6, 1), (6, 2), (6, 3)}
Given,
The sets,
A = {1, 2, 3}
B = {4, 6}
We have to find B × A.
Here,
Consider the Cartesian product:
The set of all ordered pairs (x, y) such that x belongs to A and y belongs to B is referred to as the Cartesian Product of sets A and B in mathematics. For instance, the Cartesian Product of A and B is (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), and (2, 5) if A = [1, 2] and B = [3, 4, 5].
The Cartesian product of B × A = {(b, a) | b € B, a € A}
So,
B × A = {4, 6} × {1, 2, 3}
B × A = {(4, 1), (4, 2), (4, 3), (6, 1), (6, 2), (6, 3)}
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Use the graph below to write the formula (in factored form) for a polynomial of least degree.negative even degree function. Y intercept at -3. x intercepts at -3,-2,3 and 4If you have a non-integer coefficient then write it as a fraction. Organize factors (left to right) from smallest zero to largest. Answer:
Answers
A polynomial function is in standard form when the terms in its formula are ordered from highest to lowest degree.
The factored form of a polynomial function as a function of "x" is expressed as:
[tex]f(x)=(x-a)(x-b)(x-c)(x-d)[/tex]where a, b, c, and d are the x-intercepts or zeros of the polynomial function.
From the given graph, the zeros of the polynomial graph are the point where the curve cuts the x-axis. The zeros of the polynomial are at x = -3, -2, 3 and 4
The factors of the polynomial function will be (x+3)(x+2)(x-3)(x-4)
The formula (in factored form) for a polynomial of least degree will be:
[tex]\begin{gathered} f(x)=(x-(-3))(x-(-2))(x-3)(x-4) \\ f(x)=(x+3)(x+2)(x-3)(x-4) \end{gathered}[/tex]well I'm stuck on this homework question and need help please thank you
Answers
A function can have miltiple x intercepts A function can have multiple y intercepts To find the y intercept you must find the zeros The notation of the Zeros of the function is f(0)
Answers
The statements which are true regarding a function among the given answer choices are;
A function can have multiple x-intercepts.The notation of the zeroes of the function is; f(0).Which statements among the answer choices are true for functions?It follows from the complete task content that the statements which are true be identified from the given answer choices.
From the definition of a function; A function is a relation which assigns to every input value one single output value. Hence, it follows that no single input value has more than one output value assigned to it.
It therefore follows from the definition above that; a function can have multiple x-intercepts, but can only have one y-intercept.
Also, the zeroes of the function are represented by the function instance; f(0) at which point the input, x = 0.
Remarks;
The complete task content is such that; The statements which are correct about functions are to.be identified.
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Please assist me in understanding how to solve number 4
Answers
Solution:
Given that;
y varies directly with the square of x
[tex]y\propto x^2[/tex]This expression above becomes
[tex]\begin{gathered} y=kx^2 \\ Where\text{ k is the constant} \end{gathered}[/tex]When
[tex]y=10\text{ and x}=5[/tex]Substitute the values for x and y into the expression above to find k
[tex]\begin{gathered} y=kx^2 \\ 10=k(5)^2 \\ 10=k(25) \\ 10=25k \\ Divide\text{ both sides 25} \\ \frac{25k}{25}=\frac{10}{25} \\ k=\frac{2}{5} \end{gathered}[/tex]The expression becomes
[tex]\begin{gathered} y=kx^2 \\ y=\frac{2}{5}x^2 \end{gathered}[/tex]a) The value of y when x = 20
[tex]\begin{gathered} y=\frac{2}{5}x^2 \\ y=\frac{2}{5}(20)^2 \\ y=\frac{2}{5}(400) \\ y=160 \end{gathered}[/tex]Hence, the value of y is 160
b) The value of x when y = 40
[tex]\begin{gathered} y=\frac{2}{5}x^2 \\ 40=\frac{2}{5}x^2 \\ Crossmultiply \\ 40(5)=2x^2 \\ 200=2x^2 \\ Divide\text{ both sides by 2} \\ \frac{200}{2}=\frac{2x^2}{2} \\ 100=x^2 \\ x^2=100 \\ Square\text{ root of both sides} \\ \sqrt{x^2}=\sqrt{100} \\ x=10 \end{gathered}[/tex]Hence, the value of x is 10
please help :(Find the coordinates of the midpoint of HXH(4 1/2, -4 1/4) , X(2 3/4, -2 1/4)
Answers
To find the coordinates of the midpoint of HX, we would apply the midpoint formula which is expressed as
[tex]\text{Midpoint = }\lbrack\frac{(x1\text{ + x2)}}{2},\text{ }\frac{(y1\text{ + y2)}}{2}\rbrack[/tex]From the information given,
[tex]\begin{gathered} x1\text{ = 4}\frac{1}{2}\text{ = 4.5, x2 = 2}\frac{3}{4}=\text{ 2.75} \\ y1\text{ = -4}\frac{1}{2}=-4.5,\text{ }y2=-2\frac{1}{4}=\text{ - 2.25} \\ \text{Midpoint = }\lbrack\frac{(4.5\text{ + 2.75)}}{2},\text{ }\frac{(-4.5\text{ - 2.25)}}{2}\rbrack \\ \text{Midpoint = (3.625, - 3.375)} \end{gathered}[/tex]HELP PLS (question in image)
Answers
Answer:
[tex]106-19\sqrt{x} 10[/tex]
Step-by-step explanation:
Identify the type of polar graph for the equation: r = 3-5cos θ aLimacon with inner loop bCardioid cDimpled limacon dConvex limacon eRose Curve fCircle gLemniscate
Answers
Given the equation:
[tex]r=3-5\cos \theta[/tex]Let's identify the type of polar graph for the equation.
To identify the type of polar graph, use the formula below to get the Cartesian form:
[tex](x^2_{}+y^2)=r(\cos \theta,\sin \theta)[/tex]Thus, we have:
[tex](x^2+y^2)=3\sqrt[]{x^2+y^2}-5x[/tex]We have the graph of the equation below:
We can see the graph forms a Limacon with an inner loop.
Therefore, the type of polar graph for the given equation is a limacon with inner loop.
ANSWER:
Find the negative member of the solution set for |2x -4| =6
Answers
The negative solution of the absolute value function is x = - 1.
What is the negative solution of an absolute value set?In this problem we need to solve for x in an absolute value function, whose procedure is done by the use of algebra properties:
Step 1 - Initial condition:
|2 · x - 4| = 6
Step 2 - By definition of absolute value:
2 · x - 4 = 6 or - 2 · x + 4 = 6
Step 3 - By compatibility with addition, existence of additive inverse, associative, commutative and modulative properties:
2 · x = 10 or - 2 · x = 2
Step 4 - By compatibility with multiplication, existence of multiplicative inverse, associative, commutative and modulative properties we get this result:
x = 5 or x = - 1
The negative solution of the function is x = - 1.
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what are the terms in 7h+3
Answers
Input data
7h + 3
Procedure
A term is a single mathematical expression.
3 = is a single term.
It is simply a numerical term called a constant.
7h = is also a single term. , The coefficient of the first term is 7
Evaluate.C15 3 It says I need to evaluate 15^C 3
Answers
Explanation
We are required to determine the value of the following:
[tex]_{15}C_3[/tex]This is achieved thus:
We know that the combination formula is given as:
Therefore, we have:
[tex]\begin{gathered} _{15}C_3=\frac{15!}{3!(15-3)!} \\ _{15}C_3=\frac{15!}{3!12!} \\ _{15}C_3=\frac{15\cdot14\cdot13\cdot12!}{3!12!} \\ _{15}C_3=\frac{15\cdot14\cdot13}{3!}=\frac{15\cdot14\cdot13}{3\cdot2\cdot1} \\ _{15}C_3=5\cdot7\cdot13 \\ _{15}C_3=455 \end{gathered}[/tex]Hence, the answer is:
[tex]455[/tex]Find the value of z such that 0.04 of the area lies to the right of z. Round your answer toTwo decimal places.
Answers
The total area under the normal distribution curve is 1. z-scores are indicated in the horizontal axis below this curve. This means that the sum of areas under the curve at the left and at the right of a certain z-score must be equal to 1.
Then if the area at the right of the z-score that we are looking for is 0.04 the area at its left must be equal to 1-0.04=0.96. The area at the left of z is important because z-score tables usually show the areas at the left of several z-scores. Then the only thing that we have to do is look for the z-score associated with 0.96 in one of these tables. In your case the table that you should use is the one named "Normal Table -∞ to z". That table should look like this one:
As you can see the value 0.96 is associated with the row 1.7 and the column .05 which means that the z-score that meets that the area under the curve at its right is 0.04 is z=1.7+0.05=1.75.
AnswerThen the answer is 1.75
Nayeli bought Jamba juice smoothies for herself and Evelyn after school one day. The smoothies cost $4.95 each plus 8.5% tax. how much change did she receive from a $20 bill
Answers
Explanation
Step 1
remember
[tex]8.5\text{ \%}\Rightarrow\frac{8.5}{100}=0.085[/tex]then, to find the value of the tax, multiply 4.95 0 0.085
[tex]\text{tax}=4.95\cdot0.085=0.42075\text{ per smoothie}[/tex]so, the total cost is
total =2 smoothies +(taxes for 2 smoothies)
total=(2*4.95)+(2*0.42075)
total=9.9+0.8415
total=10.7415
so, Nayebi paid $10.7415
In one us city the taxi cost is 2$ plus .50c per mile . If you are traveling from the airport there is an additional charge of 3.50$ for tolls how far can i travel for 33$
Answers
Let the number of miles I can travel for $33 be x;
The total cost of taxi ride from the airport is;
Flat fee + Tolls fee + Charge/Mile = Total cost
Flat fee = $2.00
Toll fee = $3.50
Charge per mile = 0.50x
Total cost = $33.00
Thus, we have;
[tex]\begin{gathered} 2.00+3.50+0.50x=33.00 \\ 0.50x=33.00-5.50 \\ 0.50x=27.50 \\ x=\frac{27.50}{0.50} \\ x=55 \end{gathered}[/tex]Thus, the number of miles
What is the product of 11/12 and its reciprocal?
Answers
Answer:
The product of 11/12 is 0.916.This as as a fraction would be 0.916/1.00. This means it's reciprocal is 1.
Step-by-step explanation:
The reciprocal is basically the bottom part, denominator, of the fraction, being siwtched to on top of the fraction (numerator, and vice versa. The fraction would be 0.916/ 1.00 because the closest whole number to 0.916 is 1, meaning the fraction would be 0.916 out of 1. DO NOT MISTAKE THIS FOR 100. When you do the final step, finding the recirprocal of 0.916/1.00, we siwtch the numerator and denominators position, making out answer:
The product of 11/12 is 0.916 which is 0.916/1.00 in fraction form. The reciprocal of this is 1.00/0.916. Hope this helped!
Find the slope of the line that passes through (54, -61) and (8, -56).
Answers
Answer:
The slope m of the line that passes through the two given points is;
[tex]m=-\frac{5}{46}[/tex]Explanation:
We want to calculate the slope of the line that passes through the given point;
[tex](54,-61)\text{ and }(8,-56)[/tex]Recall that the slope formula can be written as;
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]substituting the given points;
[tex]\begin{gathered} (x_1,y_1)=(54,-61) \\ (x_2,y_2)=(8,-56) \end{gathered}[/tex]We have;
[tex]\begin{gathered} m=\frac{-56-(-61)}{8-54}=\frac{5}{-46} \\ m=-\frac{5}{46} \end{gathered}[/tex]Therefore, the slope m of the line that passes through the two given points is;
[tex]m=-\frac{5}{46}[/tex]
A decrease in smoking in the United States has resulted in lower death rates caused bylung cancer. The number of death rates per 100,000 people y can be expressed byy = - 26x2 - .55x + 91.81, where x represents the number of year after 2000.
Answers
Given the equation:
[tex]y=-0.26x^2-0.55x+91.81[/tex]Where x represents the number of years after 2000.
Let's solve for the following:
a.) Calculate the number of deaths per 100,000 for 2015 and 2017.
• For 2015, we have:
Number of years between 2015 and 2000 = 2015 - 2000 = 15
Substitute 15 for x and solve for y:
[tex]\begin{gathered} y=-0.26(15)^2-0.55(15)+91.81 \\ \\ y=-0.26(225)-8.25+91.81 \\ \\ y=-58.5-8.25+91.81 \\ \\ y=25.06\approx25 \end{gathered}[/tex]The number of deaths per 100,000 for 2015 is 25.
• For 2017:
Number of years between 2017 and 2000 = 2017 - 2000 = 17 years
Subustitute 17 for x and solve for y:
[tex]\begin{gathered} y=-0.25(17)^2-0.55(17)+91.81 \\ \\ y=7.32\approx7 \end{gathered}[/tex]The number of deaths oer 100,000 for 2017 is 7.
• b.) Let's solve for x when y = 50 using the quadratic formula.
Apply the quadratic formula:
[tex]x=\frac{-b\pm\sqrt[]{(b^2-4ac)}}{2a}[/tex]Now, subsitute 50 for y and equate to zero:
[tex]50=-0.26x^2-0.55x+91.81[/tex]Subtract 50 from both sides:
[tex]\begin{gathered} 50-50=-0.26x^2-0.55x+91.81-50 \\ \\ 0=-0.26x^2-0.55+41.81 \\ \\ -0.26x^2-0.55+41.81=0 \end{gathered}[/tex]Apply the general quadractic equation to get the values of a, b and c:
[tex]\begin{gathered} ax^2+bx+c=0 \\ \\ -0.26x^2-0.55+41.81=0 \end{gathered}[/tex]Hence, we have:
a = -0.26
b = -0.55
c = 41.81
Thus, we have:
[tex]\begin{gathered} x=\frac{-(-0.55)\pm\sqrt[]{-0.55^2-4(-0.26\ast41.81)}}{2(-0.26)} \\ \\ x=\frac{0.55\pm\sqrt[]{0.3025+43.4824}}{-0.52} \\ \\ x=\frac{0.55\pm6.617}{-0.52} \\ \\ x=-13.78,\text{ 11.}67 \end{gathered}[/tex]Since the number of years cannot be a negative value, let's take the positive value 11.67
Therefore, the value of x is 11.67 when y = 50.
A consumer group feels that the average person spends less than 5 dollars each month on tooth care products. They decide to use hypothesis testing to see if they are right. Which of the following would be the alternative hypothesis?
Answers
The alternative hypothesis will be Ha : u < 5
What is an alternative hypothesis?An alternative hypothesis simply means the proposed explanation in the hypothesis test. It is used to demonstrate a particular condition.
In this case, the consumer group feels that the average person spends less than 5 dollars each month on tooth care products.
Therefore, the alternative hypothesis will be that the average is less than 5.
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11 gallons Blue Car 2 of gas 35.4 miles A gallons 27 miles Silver Car 5 14. You are running a fuel economy study. You want to find out which car can travel a greater distance on 1'gallon of gas. a. What is the gas mileage, in miles per gallon, for the blue car? b. What is the gas mileage, in miles per gallon, for the silver car? c. Which car could travel the greater distance on 1 gallon of gas?
Answers
Answer:
a) 23.67 miles per gallon
b) 34 miles per gallon
c) The silver car could travel a greater distance.
Step-by-step explanation:
a)
Conversion of the mixed numbers to fractions:
[tex]1\frac{1}{2}=\frac{1\ast2+1}{2}=\frac{2+1}{2}=\frac{3}{2}[/tex][tex]35\frac{1}{2}=\frac{35\ast2+1}{2}=\frac{70+1}{2}=\frac{71}{2}[/tex]Gas mileage:
3/2 gallons - 71/2 miles
1 gallons - x miles
Simplifying the top line by 2.
3 gallons - 71 miles
1 gallon - x miles
3x = 71
x = 71/3
x = 23.67 miles per gallon
b)
Conversion of the mixed number to fraction:
[tex]27\frac{1}{5}=\frac{27\ast5+1}{5}=\frac{135+1}{5}=\frac{136}{5}[/tex]Mileage:
4/5 gallons - 136/5 miles
1 gallon - x miles
Simplifying the top line by 5
4 gallons - 136 miles
1 gallon - x miles
4x = 136
x = 136/4
x = 34 miles per gallon
c)
Blue car: 23.67 miles per gallon
Silver car: 34 miles per gallon
Silver car could travel a greater distance.
What would -5/6 be when turned into a decimal?
Answers
Answer:
answer is -0.8333
round about -0.834
Step-by-step explanation: I hope this helps.
Answer:
there are 14 square and 18 rectangles. what is the simplest ratio of squares to rectangles?
Answers
The simplest ratio of squares to rectangles can be obtained as follows:
There are 14 squares and 18 rectangles. The ratio of squares to rectangles is:
[tex]\frac{14}{18}=\frac{7}{9}[/tex]Then, the simplest ratio is 7/9 because 7 is a prime number and the ratio cannot be simplified any more. To obtain 7/9 we divided the numerator by 2 and the denominator also by 2.
f(x) = square root of x - 5. find f^-1 (x) and it’s domain
Answers
Given:
f(x) = root x - 5
Rewrite the function using y,
[tex]y=\sqrt[]{x}-5[/tex]Now, interchange the position of x and y in the function,
[tex]x=\sqrt[]{y}-5[/tex]Isolate the dependent variable
[tex]\begin{gathered} \sqrt[]{y}=x+5 \\ y=(x+5)^2 \end{gathered}[/tex]Therefore,
[tex]f^{-1}(x)=(x+5)^2[/tex]And the domain is minus infinity to infinity
[tex]\begin{gathered} f^{-1}(x)=(x+5)^2 \\ \text{Domain}=(-\infty,\infty) \end{gathered}[/tex]Find the length of line segment MN. Round to the nearest hundredths place.
Answers
First, look th the graph and set the coordinate of the points:
M = (mx,my)= (-1,2)
N = (nx,ny)= (4,0)
Now, apply the distance formula:
[tex]\text{Distance =}\sqrt[]{(mx-nx)^2+(my-ny)^2}[/tex]Replace with the coordinates:
[tex]D\text{ =}\sqrt[]{(-1-4)^2+(2-0)^2}[/tex][tex]D=\sqrt[]{(-5)^2+2^2}=\sqrt[]{25+4}=\sqrt[]{29}\text{ =5.3}9[/tex]Distance: 5.39
Determine the common ratio for each of the following geometric series and determine which one(s) have an infinite sum.
I. 4+5+25/4+…
II. -7+7/4-7/9+…
III. 1/2-1+2…
IV. 4- ++...
A. III only
B. II, IV only
C. I, Ill only
D. I, II, IV only
Answers
The correct answer is Option A ( III Only). I . -16 sum cannot be negative, II. Not a G.P, III. Sum = 1/4, and IV. Not a G.P.
Solution:Given geometric series,
I. 4 +5 +25 /4 ….
The common ratio(r) is (5/1)/(4/1) = 5/4.
S∞ = a / ( 1 - r)
= 4 / ( 1 - 5/4)
= 4 / -1/4
S∞ = -16.
Since sum cannot be negative.
II . -7 + 7/3 - 7/9+ ....
Here common ratio = -7 / (7/3) = -1/3
but - 7/9 / 7 /3 = 7/9
Here there is no common ratio so this not a G.P.
iii. 1/2 -1 + 2.....
Common ratio = -1 / (1/2) = -2
S∞ = a / ( 1 - r)
= 1/2 / (1 -(-2))
S∞ = 1/4.
iv 4 - 8/5 +16/5.....
Here there is no common ratio.
So this is not a G.P.
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please help me and answer quick because my brainly keeps crashing before i can see the answer
Answers
The surface area of a sphere is given by the formula
[tex]SA=4*pi*r^2[/tex]we have
r=24/2=12 ft ----> the radius is half the diameter
substitute
[tex]\begin{gathered} SA=4*pi*12^2 \\ SA=576pi\text{ ft}^2 \end{gathered}[/tex]