question 1: 5 1/8 is 2/3 of what number?
question 2: what fraction of 9 3/8 is 4 3/8?
Answer:
1) [tex]7 \frac{11}{16} [/tex]
2) [tex] \frac{7}{15} [/tex]
Step-by-step explanation:
1) Let's convert the mixed fraction into a improper fraction.
[tex]5\frac{1}{8} \\ = \frac{5(8) + 1}{8} \\ = \frac{41}{8} [/tex]
Let the number be x.
[tex] \frac{2}{3} x = \frac{41}{8} \\ x = \frac{41}{8} \div \frac{2}{3} \\ x = \frac{41}{8} \times \frac{3}{2} \\ x = \frac{123}{6} \\ x = 7 \frac{11}{16} [/tex]
2)[tex]4 \frac{3}{8} = \frac{35}{8} [/tex]
[tex]9 \frac{3}{8} = \frac{75}{8} [/tex]
[tex]4 \frac{3}{8} \div 9 \frac{3}{8} \\ = \frac{35}{8} \div \frac{75}{8} \\ = \frac{35}{8} \times \frac{8}{75} \\ = \frac{7}{15} [/tex]
Robyn saves up $204 and spends $32.50 on books. She wants to purchase more books from a sale where they cost $8.15 each. Which equation represents the situation? A. 204x=8.15+32.5 B. 8.15x+32.5=204 C. 8.15+32.5x=204 D. 32.5x=204⋅8.15
Answer: B
Step-by-step explanation:
If we assume the no. of books to be x.
Value of more books will be 8.15 x
The equation will be
8.15x + 32.5 = 204
In a school auditorium, the number of chairs in a row is the same as the number of rows of chairs. There are 7033 students in the school. If we know that less than 31 chairs were empty, how many chairs were empty after all the students sat down?
Same number of rows to chairs in a row would form a square.
Use the total number of students as the area
Find the number or rows by taking the square root of student:
The square root of 7033 is 83.86
Round up to 84
Total seats would be rows x seats per row:
84 x 84 = 7,056 total seats
7056 seats - 7033 students = 23 empty seats
In the image, point A marks the center of the circle. Which two lengths must form a ratio of 1:2?
A.
A F:AE
B.
BC:EF
C.
EF:AI
D.
AI:EF
E.
AI:AD
Answer: AI:EF
Step-by-step explanation:
Answer:
D. ) AI:EF
Step-by-step explanation:
PLATO
A bowl has 85 pieces of candy. Nineteen children empty the bowl of candy. Some children take 3 pieces, some children take 5 pieces, and 1 child takes 7 pieces of candy. How many children take 3 pieces of candy?
Answer:
children take 3 pieces of candy are 6
Step-by-step explanation:
x+y=19-1 x+y=18
3x+5y=85-7 3x+5y=78
eliminate x by multiplying the first equation by 3:
3x+3y=54
3x+5y=85 subtract
(3x+3y)-(3x+6y)=54-78
3x-3y-3x-5y=-24
-2y=-24 y=-24/-2=12
y=12 , substitute for y:
x+y=18
x=18-12
x=6
check: 3x+5y=78
3(6)+5(12)=78
18+60=78 correct
WILL GIVE BRAINLIEST THANKS AND 5 STARS... PLZ HELP
Answer:
507x223 is greater than 530 x 200
914x385 is less than 900 x 400
At which root does the graph of f(x) = (x + 4) 6(x + 7)5 cross the x-axis?
-7
4
4
07
Answer:
-7 and -4
Step-by-step explanation:
The graph of the function f(x) = (x + 4)⁶ (x + 7)⁵ cross the X axis at x = -4 and x = -7.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Given is a function,
f(x) = (x + 4)⁶ (x + 7)⁵
When the function cross the X axis, the value of the function will be 0.
Let f(x) = 0
(x + 4)⁶ (x + 7)⁵ = 0
This implies that, either x + 4 = 0 or x + 7 = 0
x + 4 = 0 ⇒ x = -4
x + 7 = 0 ⇒ x = -7
Hence the roots are -4 and -7 where the function crosses the X axis.
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which of the following shows the polynomial below written in descending order?
Answer:
A
Step-by-step explanation:
Descending order is where the monomials of a polynomial are arranged in decreasing exponent order so the answer is A.
Answer:
the answer is option a because all the expression in option a is written descending power form.
There are only green pens and red pens in a box. there are 3 more red pens than green pens in the box. sheila is going to take at random two pens from the box the probability that sheila will take two pens of the same color is 17/35 work out two different numbers of green pens that could be in the box
Answer: 6 or 9
Step-by-step explanation:
Given the following :
Let the number of green pens = x
Number of red pens = x + 3
Probability of picking same color = 17/35
Taking two pens at random; probability of picking two pens of same color.
Probability of picking red on first pick then red on second pick ; or picking blue on first pick then blue on second pick
Probability = (Required outcome / Total possible outcomes)
Total number of pens = x + x + 3 = 2x + 3
Probability of picking red then red:
P(red first) = (x+3)/2x+3
P(red second) = x+3-1 / 2x+3-1 = (x+2)/2x+2)
Therefore, probability of red then red =
(x+3)/(2x+3) × (x+2)/2x+2)
= (x+3)(x+2) / (2x+3)(2x+2)
Probability of green then green:
P(first green) = x/(2x+3)
P(second green) = (x-1) / (2x+3-1) = (x-1) / (2x+2)
P(green then green) = x(x-1)/(2x+3)(2x+2)
Therefore,
[(x+3)(x+2) / (2x+3)(2x+2)] + [x(x-1)/(2x+3)(2x+2)] = 17/35
(x+3)(x+2)+x(x-1) / (2x+3)(2x+2) = 17/35
Cross multiply :
35(x+3)(x+2)+x(x-1) = 17(2x+3)(2x+2)
35(2x^2 + 4x + 6) = 17(4x^2 + 10x + 6)
70x^2 + 140x + 210 = 68x^2 + 170x + 102
70x^2 - 68x^2 + 140x - 170x + 210 - 102 = 0
2x^2 - 30x + 108 = 0
Now we have a quadratic equation which can be factoeized used using any known factorization method.
Factorizing this, we get
(x-6) = 0 or (x-9) = 0
x = 6 or x = 9
: An Australian man on holiday in Germany finds that his wallet
contains 700 AUD. If he changes the money at a bank how
many euros will he receive?
Answer:
700 AUD ⇒ 430.72 euros
Hope this helps.
PLS HELP ASAP The following probability distribution table shows information collected from a survey of students regarding their grade level and the transportation they use to arrive at school. What is the probability that a randomly selected eighth grader takes the bus?
Answer:
44%
Step-by-step explanation:
For these types of problems, look at the totals. We know that there are 0.44 out of 1 eighth graders. Since it doesn't specify how the 8th grader is dropped off, we take 0.44 and divide it by 1 (the total). We get 0.44, but since it's most likely asking for percentages, multiply that by 100.
What is the ratio of the Volume of the smaller pyramid to the larger pyramid
Square all the integers from 1 to 10 inclusive. Then, round each number to the nearest hundred. Finally, sum the numbers. What do you get?
Answer:
22.467
Step-by-step explanation:
Hello,
You just have to do the computation in XL or using a calculator, and round each number to the nearest hundred
x sqrt(x)
1 1
2 1.414
3 1.732
4 2
5 2.236
6 2.449
7 2.646
8 2.828
9 3
10 3.162
and do the sum which is 22.467
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
300
Step-by-step explanation:
First let's square all the integers from 1 to 10 inclusive. We get:
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
8^2 = 64
9^2 = 81
10^2 = 100.
Rounding to the nearest hundred, we get that 1, 4, 9, 16, 36, and 49 all round to 0 and 64, 81, and 100 round to 100.
Therefore, we obtain
0+0+0+0+0+0+0+100+100+100,
or 300.
need help with this question, i dont think its hard for you.
Find the total surface area of this triangular prism...
Answer:
144 cm^2
Step-by-step explanation:
8x6+4x10+4x8+4x6
48+40+32+24
80+40+24
120+24
144
If the number of bacteria in a colony doubles every 10 hours and there is currently a population of 300 bacteria, what will the population be 20 hours from now?
Answer:
1200 bacteria
Step-by-step explanation:
20 hours divided by 10 hours = 2, so it will be doubled two times.
300 times 2 for the first doubling = 600
600 times 2 for the second doubling = 1200
Consider triangle ABC. Triangle A B C. Angle C is 80 degrees and angles B and A are y degrees. What is the value of y in the triangle? Angle y = °
Answer:
y is equal to 50 degrees.
Step-by-step explanation:
The sum of the angles of a triangle is always 180 degrees. To find what y is, subtract 80 from 180 and divide the difference by 2. This will give you 50 degrees.
Answer:
y= 50°
Step-by-step explanation:
∠A =∠B = y. So, ΔABC is an isosceles triangle.
Sum of angles of triangle = 180
∠A + ∠B + ∠C = 180
y + y + 80 = 180 {add like terms}
2y + 80 = 180 {Subtract 80 from both sides}
2y + 80 - 80 = 180 - 80
2y = 100 {divide both sides by 2}
2y/2 = 100/2
y= 50°
A Rosa le gusta jugar con su primo Eduardo utilizando números. Rosa le planteó encontrar dos números que sumados den 15 y que el doble de uno de ellos sea igual al otro más 3 unidades, ¿De qué números se trata?
Answer:
Los números son 6 y 9
Step-by-step explanation:
Este problema se puede resolver por medio de un sistema de ecuaciones.
El primer número será x y el segundo número será y.
Sabemos que los dos números suman 15, por lo tanto esto se puede escribir como:
[tex]x+y=15[/tex]
Por otro lado sabemos que el doble de uno de ellos es igual al otro más 3 unidades, esto lo podemos escribir de la siguiente manera:
[tex]2x=y+3[/tex] (el doble del primero es igual al segundo más 3)
Reescribiendo esta segunda ecuación tenemos:
[tex]2x-y=3[/tex]
Por lo tanto, nuestras dos ecuaciones son:
[tex]x+y=15\\2x-y=3[/tex]
Resolviendo el sistema por el método de reducción observamos que, si sumamos ambas ecuaciones, las y se cancelan y quedamos con:
[tex]3x=18\\x=6[/tex]
Ahora, sustituimos este valor en la primera ecuación para obtener el valor de y:
[tex]x+y=15\\6+y=15\\y=15-6\\y=9[/tex]
Por lo tanto, los números son 6 y 9
Por medio de un sistema de ecuaciones, hay qué los números son 6 y 9.
Los números son desconocidos, por lo tanto, llaremos un de x, otro de y.Los números sumados den 15, o sea:
[tex]x + y = 15[/tex]
El doble de uno de ellos sea igual al otro más 3 unidades, o sea:
[tex]2x = y + 3[/tex]
[tex]y = 2x - 3[/tex]
Reemplazando en la primera ecuación:
[tex]x + y = 15[/tex]
[tex]x + 2x - 3 = 15[/tex]
[tex]3x = 18[/tex]
[tex]x = \frac{18}{3}[/tex]
[tex]x = 6[/tex]
[tex]y = 2x - 3 = 2(6) - 3 = 12 - 3 = 9[/tex]
Los números son 6 y 9.
Un problema similar es dado en https://brainly.com/question/24646137
If (ax+b)(bx+a)=26x^2+ Box(x) +26, where a, b, and Box are distinct integers, what is the minimum possible value of Box, the coefficient of x?
Question in latex: If $(ax+b)(bx+a)=26x^2+\Box\cdot x+26$, where $a$, $b$, and $\Box$ are distinct integers, what is the minimum possible value of $\Box$, the coefficient of $x$?
Answer:
16.59
Step-by-step explanation:
Given:
[tex](ax+b)(bx+a)=26x^2+\Box\cdot x+26[/tex]
Expanding the left hand side, we have:
[tex](ax+b)(bx+a)=abx^2+a^2x+b^2x+ab\\=abx^2+(a^2+b^2)x+ab\\=26x^2+\Box\cdot x+26\\ab=26 \implies b=\frac{26}{a}[/tex]
Therefore:
[tex]a^2+b^2=a^2+\dfrac{26}{a} =\dfrac{a^3+26}{a}[/tex]
To find the minimum value, we take the derivative and solve for its critical point.
[tex]\frac{d}{da} (\frac{a^3+26}{a})=\frac{2a^3-26}{a^2}\\$Setting the derivative equal to zero, we have:\\2a^3-26=0\\2a^3=26\\a^3=13\\a=\sqrt[3]{13}[/tex]
Recall that:
[tex]\Box=a^2+b^2=\dfrac{(\sqrt[3]{13}) ^3+26}{\sqrt[3]{13}}\\=\dfrac{13+26}{\sqrt[3]{13}}\\\\\Box=16.59[/tex]
The minimum possible value of the coefficient of x is 16.59.
Answer:
173
Step-by-step explanation:
For sympliciy let the box equal y.
Expanding the left side we get (a*x+b)(b*x+a) = (a*b*(x)^2 + (a^2 + b^2)x + a*b). Hence we have that (a*b*(x)^2 + (a^2 + b^2)x + a*b) = 26*(x)^2 + x*y + 26. Scince the coefficients of like terms in our equation must be equal, ab=26. Hence (a,b) = (1,26),(26,1),(-1,-26),(-26,-1),(2,13),(13,2),(-2,-13),(-13,-2). Since a^2 + b^2 = y we can see that the only 2 values of y are 677 and 173 (by simply plug in the values of (a,b)), taking the smaller of the two our answer is [173].
which shape is a parallelogram?
Answer:
A,C,and D are parralelograms
The parallelogram are shapes with figures having opposite sides which are parallel
What is a Parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
The sum of angles of a parallelogram is 360°
The four types are parallelograms, squares, rectangles, and rhombuses
Properties of Parallelogram
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent.
Same-Side interior angles (consecutive angles) are supplementary
Each diagonal of a parallelogram separates it into two congruent triangles
The diagonals of a parallelogram bisect each other
Given data ,
Let the parallelogram be represented as ABCD
Now , from the figure 1
a)
The figure is having opposite sides are parallel
where AB = CD
And , BC = AD
So , it is a parallelogram
b)
The figure does not have any sides parallel
So , it is not a parallelogram
c)
The shape is having 2 sides as parallel
And , AB = CD
So , it is a parallelogram
d)
The shape is having 2 sides as parallel
And , AB = CD
So , it is a parallelogram
Hence , the parallelogram is solved
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An interior angle of a regular convex polygon is 140°. How many sides does the polygon have?
Answer:
hope it will help uh.....
A trapezoid has a base length of 22 cm and a mid-segment length of 23 cm. What is the length of the other
base?
24 cm
26 cm
22 cm
28 cm
Answer:
24 cm
Step-by-step explanation:
Let the length of other base be x cm
Therefore, by mid segment formula of a trapezoid, we have:
[tex]23 = \frac{1}{2} (x + 22) \\ \\ 23 \times 2 = x + 22 \\ 46 = x + 22 \\ 46 - 22 = x \\ x = 24 \: cm[/tex]
4x - 1
2.
= x + 7
Can someone help please?
Answer:
6[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
4x-12 = x+7
4x-12+12 = x+7+12
4x = x+19
4x-x = x+19-x
3x=19
x = 6[tex]\frac{1}{3}[/tex]
And if we substitute the value of x into the equation 4x-12 = x+7,
we will get 13[tex]\frac{1}{3}[/tex] = 13[tex]\frac{1}{3}[/tex] in the end.
Hope this helps :)
Help please on linear math
Answer:
D
Step-by-step explanation:
[tex]y=\frac{-9x-5}{-8}[/tex]
factoring out a negative[tex]y=\frac{9x+5}{8}[/tex]
Answer:
[tex] \frac{5}{8} [/tex]Option D is the correct option.
Step-by-step explanation:
Given that
9x - 8y = 0
finding y-intercept
put x = 0 , we get
9(0) - 8y + 5 = 0
Calculate the product
-8y + 5 = 0
Move the constant to L.H.S and change its sign
-8y = 0 - 5
Calculate the difference
-8y = -5
divide both sides of the equation by -8
-8y/-8 = -5/-8
Calculate
y = 5/8
Hope this helps...
Good luck on your assignment...
What is the solution of the following system 5x+2y+z=4 x+2z=4 2x+y-z=-1
Let us take the 2nd equation.
x + 2z = 4
x = 4 - 2z
Let us substitute this value of x in equation 1.
5x + 2y + z = 4
5(4-2z) + 2y + z = 4
20 - 10z + 2y + z = 4
2y - 9z + 20 = 4
2y = 9z - 16
y = (9z - 16)/2
Let us substitute this value of y, as well as that of x that we used earlier, in the third equation.
2x + y - z = -1
2(4-2z) + (9z-16)/2 + z = -1
8 - 4z + (9z/2) - 8 + z = -1
Let us multiply both sides of this equation by 2.
16 - 8z + 9z - 16 + 2z = -2
3z = -2
z = [tex]\frac{-2}{3}[/tex]
x = 4 - 2z
= 4 + [tex]\frac{4}{3}[/tex]
= [tex]\frac{16}{3}[/tex]
y = (9z-16)/2
= ([tex]\frac{-18}{3}[/tex] - 16)/2
= ( [tex]\frac{-66}{3}[/tex])/2
= -22/2
= -11
Therefore, x = [tex]\frac{16}{3}[/tex], y = -11, and z = [tex]\frac{-2}{3}[/tex].
Clinical literature reports that the duration of a typical cold is roughly 18 days. Researchers wanted to know if people tend to underestimate the duration of a typical cold, on average. They surveyed a random sample of 352 healthy adults in Georgia and asked them how long they think that a typical cold lasts. The researchers reported a 95% confidence interval of 6.9 to 8.2 days for the mean expected duration of typical cold. The researchers reported that the answers to this question were strongly right-skewed. The 95% confidence interval (6.9, 8.2) they obtained is
Answer:
The 95% confidence interval (6.9, 8.2) they obtained means that "We are 95% confident that the population mean duration is between 6.9 and 8.2 days".
Option B from the complete Question.
Step-by-step explanation:
Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
Critical value will be obtained using the t-distribution if there is no information provided for the population standard deviation and it is obtained from the z-tables if the population standard deviation is known or the sample size is large enough that the sample properties can be approximated to be the same as the population properties.
Standard error of the mean = σₓ = (σ/√n)
σ = standard deviation of the sample
n = sample size
Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
So, the confidence interval (6.9, 8.2) obtained in the question means that "We are 95% confident that the population mean duration is between 6.9 and 8.2 days".
Hope this Helps!!!
in the function equation ff (xx ) = 1500 (1.43)^xx, is it growth or decay? what is the percent of the growth/decay? what is the initial value?
Answer:
The initial value is 1500
growth
43 % growth
Step-by-step explanation:
Exponential equations are in the form
y = a * b^x
a is the initial value
b is the growth or decay
b>1 is growth b-1 rate of growth
b <1 decay 1-b rate of decay
f(x) = 1500 * 1.43 ^x
The initial value is 1500
1.43 > 1 so it is growth
1- 1.43 = .43
Change to percent
43 % growth
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 2−x and y = 4x + 3 intersect are the solutions of the equation 2−x = 4x + 3. (4 points) Part B: Make tables to find the solution to 2−x = 4x + 3. Take the integer values of x only between −3 and 3. (4 points) Part C: How can you solve the equation 2−x = 4x + 3 graphically? (2 points) PLez Answer 50 points
Answer:
Step-by-step explanation:
Part A:
We have two lines: y = 2 - x and y = 4x + 3 . Given two equations that are both required to be true. The answer is the points where the lines cross, this means we have to make the equations equal to each other. It will look like this:
2 - x = 4x + 3
Part B:
In order to solve the equation we need to put the like terms together. So we will add x on each side.
2 - x = 4x + 3
+x +x
So now we get:
2 = 5x + 3
Now that x is on one side and is positive we will move 3 on the left side by subtracting it from each side.
2 = 5x + 3
-3 -3
So now we get:
-1 = 5x
Now that the like terms have been combined we need to find out what x alone is so we divide 5 on each side:
[tex]\frac{-1}{5}[/tex] = [tex]\frac{5x}{5}[/tex]
No we see that:
x = [tex]-\frac{1}{5}[/tex]
A top view of two walls of a room is represented by the x and y-axis, with units in meters. A ball is rolled from the point (0,15). It hits the adjacent wall at (20,0). Find the absolute value function that models the path of the ball. Determine when the ball passes within 3 meters of the wall represented by the x-axis.
Answer:
The absolute value function that models the path of the ball is
[tex]f(x) = \left | -\frac{3}{4}\cdot x + 15 \right |[/tex]
The coordinates when the ball passes within 3 meters of the wall is [tex]\left (3, 12\tfrac{3}{4} \right )[/tex]
Step-by-step explanation:
Given that the ball rolls without other external influences, we have;
(y - 0) = (x - 15)
The slope, m is give by the relation;
m = (y₂ - y₁)/(x₂ - x₁)
m = (15 - 0)/(0-20) = -3/4
The equation of the path of the ball in slope and intercept form is presented as follows;
y = m·x + c
15 = -3/4 ×0 + c = 15
c = 15
The absolute value function that models the path of the ball is then;
[tex]f(x) = \left | -\frac{3}{4}\cdot x + 15 \right |[/tex]
The vale of the function when x = 3 is given by the relation
[tex]f(x) = \left | -\dfrac{3}{4}\times 3 + 15 \right | = \dfrac{51}{4}[/tex]
Therefore, we have the coordinates as [tex]\left (3, 12\tfrac{3}{4} \right )[/tex].
A line is defined by the equation y = two-thirds x minus 6. The line passes through a point whose y-coordinate is 0. What is the x-coordinate of this point? A coordinate plane.
Answer:
9
Step-by-step explanation:
Put the given information into the equation and solve for x.
y = (2/3)x -6
0 = (2/3)x -6 . . . . . substitute for y
0 = x - 9 . . . . . . . . multiply by 3/2
9 = x . . . . . . . . . . . .add 9
The x-coordinate of the x-intercept point is 9.
Answer:
x=9
hope this helps :>