Equations:
1. (30)(5)= 150
2. 30 + 30 + 30 + 30 + 30 = 150
I round:
30 dollars divided by 5 rounds = 6 dollars per round.
The total amount spent by the two boys is $300.
What is algebraic expression?An expression in mathematics is a combination of terms both constant and variable. For example, we can write the expressions as -
2x + 3y + 5
2z + y
x + 3y
Given is that Tyler and Gabe went to the arcade and played the same two games. Tyler played five rounds of each game for 30$.
We can write the total amount spent by the two boys as -
total amount = 2 x cost of each game x total number of games played
total amount = 2 x 30 x 5
total amount = 10 x 30
total amount = 300
Therefore, the total amount spent by the two boys is $300.
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What is the vertex of the parabola graphed
below?
-4-2 o
2 4
(2,0)
(2,-4)
0 (-4,0)
(4,0)
Other:
Answer:
Step-by-step explanation:
The vertex is either the highest point on the parabola or the lowest point. We have a positive parabola, so the vertex is a low point. It sits at (2, -4). Locate that point and see what I mean by the lowest point on the parabola.
Solve for xxx.
x=x=x, equals
Answer:
Step-by-step explanation:
BC/AB = DE/AD
1/2 = x/(2+1)
x = 1.5
[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]
See this attachment
A 39-foot ladder is leaning against a vertical wall. If the bottom of the ladder is being pulled away from the wall at the rate of 2 feet per second, at what rate is the area of the triangle formed by the wall, the ground, and the ladder changing, in square feet per second, at the instant the bottom of the ladder is 15 feet from the wall?
Answer:
The area of the triangle formed is increasing at a rate of 29.75 square feet per second.
Step-by-step explanation:
A 39-foot ladder is leaning against a vertical wall. We are given that the bottom of the ladder is being pulled away at a rate of two feet per second, and we want to find the rate at which the area of the triangle being formed is is changing when the bottom of the ladder is 15 feet from the wall.
Please refer to the diagram below. x is the distance from the bottom of the ladder to the wall and y is the height of the ladder on the wall.
According to the Pythagorean Theorem:
[tex]\displaystyle x^2+y^2=1521[/tex]
Let's take the derivative of both sides with respect to time t. Hence:
[tex]\displaystyle \frac{d}{dt}\left[x^2+y^2\right] = \frac{d}{dt}\left[ 1521\right][/tex]
Implicitly differentiate:
[tex]\displaystyle 2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 0[/tex]
Simplify:
[tex]\displaystyle x\frac{dx}{dt} + y \frac{dy}{dt} = 0[/tex]
The area of the triangle formed will be given by:
[tex]\displaystyle A = \frac{1}{2} xy[/tex]
Again, let's take the derivative of both sides with respect to time t:
[tex]\displaystyle \frac{dA}{dt} = \frac{d}{dt}\left[\frac{1}{2}xy\right][/tex]
From the Product Rule:
[tex]\displaystyle \frac{dA}{dt} = \frac{1}{2}\left(y\frac{dx}{dt} + x\frac{dy}{dt}\right)[/tex]
At that instant, the ladder is 15 feet from the base of the wall. So, x = 15. Using this information, find y.
[tex]\displaystyle y = \sqrt{1521-(15)^2}=36[/tex]
The bottom of the ladder is being pulled away from the wall at a rate of two feet per second. So, dx/dt = 2. Using this information and the first equation, find dy/dt:
[tex]\displaystyle \frac{dy}{dt} =-\frac{x\dfrac{dx}{dt}}{y}[/tex]
Evaluate for dy/dt:
[tex]\displaystyle \frac{dy}{dt} = -\frac{(15)(2)}{(36)}=-\frac{5}{6}[/tex]
Finally, using dA/dt, substitute in appropriate values:
[tex]\displaystyle \frac{dA}{dt} = \frac{1}{2}\left((36)(2)+(15)\left(-\frac{5}{6}\right)\right)[/tex]
Evaluate. Hence:
[tex]\displaystyle \frac{dA}{dt} = \frac{119\text{ ft}^2}{4\text{ s}} = 29.75\text{ ft$^2$/s}[/tex]
The area of the triangle formed is increasing at a rate of 29.75 square feet per second.
Which is the correct calculation of the y-coordinate of point A? 0 (0 - 0)2 + (1 - y2 = 2 O (0 - 1)² + (0- y2 = 22 (0-0)² + (1 - y2 = 2 (0 - 1)2 + (0-y2 = 2
Answer:
The y-coordinate of point A is [tex]\sqrt{3}[/tex].
Step-by-step explanation:
The equation of the circle is represented by the following expression:
[tex](x-h)^{2}+(y-k)^{2} = r^{2}[/tex] (1)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]h[/tex], [tex]k[/tex] - Coordinates of the center of the circle.
[tex]r[/tex] - Radius of the circle.
If we know that [tex]h = 0[/tex], [tex]k = 0[/tex] and [tex]r = 2[/tex], then the equation of the circle is:
[tex]x^{2} + y^{2} = 4[/tex] (1b)
Then, we clear [tex]y[/tex] within (1b):
[tex]y^{2} = 4 - x^{2}[/tex]
[tex]y = \pm \sqrt{4-x^{2}}[/tex] (2)
If we know that [tex]x = 1[/tex], then the y-coordinate of point A is:
[tex]y = \sqrt{4-1^{2}}[/tex]
[tex]y = \sqrt{3}[/tex]
The y-coordinate of point A is [tex]\sqrt{3}[/tex].
Kids with cell phones: A marketing manager for a cell phone company claims that the percentage of children aged 8-12 who have cell phones differs from 52%. In a survey of 832 children aged 8-12 by a national consumers group, 449 of them had cell phones. Can you conclude that the manager's claim is true? Use the a 0.10 level of significance and the P-value method. 1. State the appropriate null and alternate hypotheses.2. Compute the test statistic.
Answer:
Low-value method
Step-by-step explanation:
consumers group
el teorema de wilson
Answer:
En matemáticas, especialmente en la teoría de números hay una proposición que vincula tres conceptos: primalidad, factorial de un número entero no nulo y congruencia de números respecto de un módulo.
answer-Wilson's theorem, in number theory, theorem that any prime p divides (p − 1)! ... + 1, where n! is the factorial notation for 1 × 2 × 3 × 4 × ⋯ × n. For example, 5 divides (5 − 1)!
Find the percentile rank for each test score in the data set. 12, 28, 35, 42, 47, 49, 50 What value corresponds to the 60th percentile
Answer:
Percentile rank:
12 = 7th
28 = 21st
35 = 36th
42 = 50th
47 = 64th
49 = 79th
50 = 93rd
- Vth number i.e. 47 is the value that corresponds to the 60th percentile.
Step-by-step explanation:
As we know,
Percentile rank = [(Number of values below x) + 0.5]/total number of values * 100
For 12,
Percentile rank = [0 + 0.5]/7 * 100
= 7th
For 28,
Percentile rank = [1 + 0.5]/7 * 100
= 21st
For 35,
Percentile rank = [2 + 0.5]/7 * 100
= 36th
For 42,
Percentile rank = [3 + 0.5]/7 * 100
= 50th
For 47,
Percentile rank = [4 + 0.5]/7 * 100
= 64th
For 49,
Percentile rank = [5 + 0.5]/7 * 100
= 79th
For 50,
Percentile rank = [6 + 0.5]/7 * 100
= 93rd
Now,
n = 7
60th percentile = 60% of n
So,
60% of n = 60/100 * 7
= 0.6 * 7
= 4.2
After rounding it off,
5th value is the 60th percentile i.e. 47.
Solve for x Solve for x Solve for x
9514 1404 393
Answer:
x = 3
Step-by-step explanation:
The two right triangles share angle A, so the similarity statement can be written ...
ΔABC ~ ΔADE
Corresponding sides are proportional, so we have ...
BC/DE = AB/AD
x/12 = 3/(3+9)
x = 3 . . . . . . . . . . multiply by 12
Answer:
x=3
this is correct!!!
I need to know the answer and the work it asks for
Answer:
b 25x6 = 150
25 decreases every month so
150 decreses every 6 month
800-150
650 are the bees remaining after 6 month
please solve this fast
Step-by-step explanation:
1.
[tex]qr - pr \: + qs - ps[/tex]
[tex]r(q - p) + s(q - p)[/tex]
[tex](r + s)(q - p)[/tex]
2.
[tex] {x}^{2} + y - xy - x[/tex]
[tex] {x}^{2} - x - xy + y[/tex]
[tex]x(x - 1) - y(x - 1)[/tex]
3.
[tex]6xy + 6 - 9y - 4x[/tex]
[tex] - 4x + 6 + 6xy - 9y[/tex]
[tex]2( - 2x + 3) - 3y( - 2x + 3)[/tex]
[tex](2 - 3y)( - 2x + 3)[/tex]
4.
[tex] {x}^{2} - 2ax - 2ab + bx[/tex]
[tex]x(x - 2a) - b(x - 2a)[/tex]
[tex]-(x +b)(2a-x)[/tex]
5.
[tex]axy + bcxy - az - bcz[/tex]
[tex]xy(a + bc) - z(a + bc)[/tex]
[tex](xy - z)(a + bc)[/tex]
James, Aimee and Zack have
weighed their suitcases. Each
weighs a prime number of
kilograms and the total weight
is 40kg.
an
What's the difference between
the lightest and heaviest
suitcase?
Answer:
29Kg
Step-by-step explanation:
P1=2Kg
P2=7Kg
P3=31Kg
P3-P1=29Kg
To find P1, P2 and P3 I started assigning the first prime number, 2, to P1 and tried to assign prime numbers to P2 and P3 so that the sum was 40, increasing them at each step.
I was lucky and I got the result after few steps :-)
find the area of this unusual shape.
Answer:
104 m^2
Step-by-step explanation:
First find the area of the rectangle
A = l*w = 10*8 = 80
Then find the area of the triangle
A = 1/2 bh = 1/2 (8) * 6 = 24
Add the areas together
80+24 = 104 m^2
Which equation has a constant of proportionality equal to 2?
Answer:
[tex]{ \tt{y = 2x}}[/tex]
Answer:
2y=x
Step-by-step explanation:
(c³d)a(cd⁷)a
Simplify
Answer:
= c^4 d^8 a^2
Step-by-step explanation:
Apply exponent rule: aa= a^2
= c^3 da^2 cd^7
= c^4 da^2 d^7
= c^4 d^8 a^2
In a quiz , positive marks are given for correct answers and negative marks are given dor incorrect answers. If Jack's scores in five successive rounds were 25,-5,-10, 15 and 10 , what was the total at the end.
I need it fast
Given:
Jack's scores in five successive rounds were 25,-5,-10, 15 and 10.
To find:
The total score at the end.
Solution:
It is given that the scores in five successive rounds were 25,-5,-10, 15 and 10. So, the sum of the scores at the end is:
[tex]Sum=25+(-5)+(-10)+15+10[/tex]
[tex]Sum=(25+15+10)+(-5-10)[/tex]
[tex]Sum=50+(-15)[/tex]
[tex]Sum=50-15[/tex]
[tex]Sum=35[/tex]
Therefore, the total score at the end. is 35.
find the value of n, if (n+1)! = 6*(n-1)!
Answer:
2
Step-by-step explanation:
(n+1)!=1×2×...×(n-1)×n×(n+1)
6*(n-1)!=1×2×...×(n-1)
--> n×(n+1)=6
-->n=2
Help please
Please help
9514 1404 393
Answer:
4. True
5. False
Step-by-step explanation:
4. The number of x-intercepts produced by the quadratic formula may be 0, 1, or 2. It will be 0 if the two roots are complex. It will be 1 if the two roots lie in the same place (one root with multiplicity 2). It is true that there may be only one x-intercept.
__
5. The value of 'b' in the quadratic formula is the coefficient of the linear term. In the given quadratic, it is -5, not 5.
if f(x)=√x-x and g(x)=2x^3-√x-x find f(x)-g(x)
Answer:
2sqrt(x)-2x^3
Step-by-step explanation:
f(x) - g(x) = sqrt(x)-x-(2x^3)+sqrt(x)+x=2sqrt(x)-2x^3
The difference of the two functions f(x) and g(x) is -
f(x) - g(x) = [tex]-2x^{3} + 2\sqrt{x}[/tex]
We have - two functions of [tex]x[/tex] :
[tex]f(x)=\sqrt{x} -x\\g(x) = 2x^{3} - \sqrt{x} -x[/tex]
We have to find -
[tex]f(x)-g(x)[/tex]
What do you understand by the term - [tex]y=f(x)\\[/tex] ?The term [tex]y=f(x)[/tex] indicates that [tex]y[/tex] is expressed as a function of [tex]x[/tex], where [tex]x[/tex] is a independent variable and [tex]y[/tex] is a dependent variable which depends on [tex]x[/tex].
According to question -
[tex]f(x)-g(x)=\sqrt{x} -x - (2x^{3} - \sqrt{x} -x)\\f(x)-g(x)=\sqrt{x} -x-2x^{3} + \sqrt{x} +x\\f(x)-g(x)=-2x^{3} + 2\sqrt{x}[/tex]
Hence, f(x) - g(x) = [tex]-2x^{3} + 2\sqrt{x}[/tex]
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At 2pm, the temperature was 9°F. At 11pm, the temperature was -11°F. What was the change in
temperature?
Answer:
21 degrees
Step-by-step explanation:
I did it on the calculator
I’m honestly not the best at math, can someone help?
Answer:
1/8
Step-by-step explanation:
Using the factor tree, we see that there is 8 possible outcomes ( right hand side)
There is only 1 way to go from left to right and have 3 wins
P(3 wins) = good outcomes / total
=1/8
During a certain 9-year period, the Consumer Price Index (CPI) decreased by
45%, but during the next 9-year period, it decreased by only 5%. Which of
these conditions must have existed during the second 9-year period?
A. Deflation
B. Stagnation
C. Conflation
D. Inflation
Answer:
deflation ,,,,
Step-by-step explanation:
I hope it's helpful for you ☺️Deflation must have existed during the second 9-year period.
What is deflation?Deflation is a decrease in the general price level of goods and services in an economy over a period of time. This means that the purchasing power of money increases, as the same amount of money can buy more goods and services.
The opposite of inflation, which is an overall rise in the cost of goods and services over time, is deflation. Money loses value due to inflation, whereas it gains value due to deflation. Deflation can reduce demand for goods and services, though, if it lasts for a long time. This is because customers may put off purchases in expectation of cheaper costs. A downturn in economic activity may follow, which would be bad for the economy.
Given data ,
Deflation is a decrease in the general price level of goods and services in an economy over a period of time. A decrease in the Consumer Price Index (CPI) is a measure of deflation.
In the first 9-year period, the CPI decreased by 45%, which indicates a significant deflationary period. In the next 9-year period, the CPI decreased by only 5%, which still indicates a deflationary period, but not as severe as the previous one.
Hence , the process is deflation in the second year
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0.
DETAILS
Model the data using an exponential function f(x) = Ab".
X
0
1
2
f(x)
400
240
144
f(x) =
Need Help?
Read It
Which recursive formula can be used to generate the sequence below, where f(1) = 3 and n ≥ 1?
3, –6, 12, –24, 48,
Answer:
f (n + 1) = -2 f(n)
Step-by-step explanation:
F(x) = 4x^3 + 7x^2-2x-1
G(x) = 4x-2
Find (f-g)(x)
HHHEELPP HELP HELP!!
I need the answer ASAP!!!!
Answer:
Step-by-step explanation:
B because the vertex is at point (3, 4) which is greatest.
Answer:
[tex]\text{b. } y=-(x-3)^2+4[/tex]
Step-by-step explanation:
Algebraically, we want to compare the y-coordinates of the vertex, since all the functions shown are parabolas that are concave down.
Let's break the format down:
The negative sign in front of each of the functions indicate that the parabolas will be concave down (open downwards), which means the vertex represents the function's maximum. The term inside the parentheses when applicable to just indicates the horizontal/phase shift.
Since the first term being squared is negative, we want to minimize its value to produce the greatest possible y-value.
Therefore, substitute whatever value of [tex]x[/tex] that makes each [tex]x^2[/tex] term equal to 0. (Maximum value of [tex]-x^2[/tex] is 0).
Therefore, we can simplify compare the last terms in each equation.
Equation A's last term is 3.
Equation B's last term is 4.
Equation C's last term is -5.
Equation D's last term is 0.
Since equation B has the greatest last term, it will have the greatest possible y-value.
f(x) = x ^ 2 - x - 6; g(x) = 2x ^ 2 + 5x + 2 Find: (f/g)(X)
Answer:
[tex](\frac{f}{g})(x) = \frac{x- 3}{2x + 1}[/tex]
Step-by-step explanation:
Given
[tex]f(x) =x^2 -x - 6[/tex]
[tex]g(x) = 2x^2 + 5x + 2[/tex]
Required
[tex](\frac{f}{g})(x)[/tex]
This is calculated as:
[tex](\frac{f}{g})(x) = \frac{f(x)}{g(x)}[/tex]
So, we have:
[tex](\frac{f}{g})(x) = \frac{x^2 - x - 6}{2x^2 + 5x + 2}[/tex]
Expand
[tex](\frac{f}{g})(x) = \frac{x^2 +2x - 3x - 6}{2x^2 + 4x+x + 2}[/tex]
Factorize
[tex](\frac{f}{g})(x) = \frac{x(x +2) - 3(x + 2)}{2x(x + 2)+1(x + 2)}[/tex]
Factor out x + 2
[tex](\frac{f}{g})(x) = \frac{(x- 3)(x + 2)}{(2x + 1)(x + 2)}[/tex]
Cancel out x + 2
[tex](\frac{f}{g})(x) = \frac{x- 3}{2x + 1}[/tex]
I need help with this
Answer: D
Step-by-step explanation:
When a coordinate is reflected over the y-axis, it changes from (x, y) to (-x, y)
The three coordinates of ΔCDE are
C = (-8, -1)D = (-6, -5)E = (-2, -4)After the y-axis reflection, they'll become:
C' = (-(-8), -1) = (8, -1)D' = (-(-6), -5) = (6, -5)E' = (-(-2), -4) = (2, -4)I hope this is correct :\
Selena's gross annual salary as the Content editor of a fashion Magazine is Rs 40000 she contribute 10% of her salary. before she pays taxes to a retirement account 25% of her remaining salary is then consumed in state and federal taxes. what is the selenas annual in take home salary if she also has to pay Rs 30 for health Insurance each month.
Answer:
Selena's annual intake home salary is $ 26,640.
Step-by-step explanation:
Since Selena's gross annual salary as the content editor of a fashion Magazine is $ 40,000, and she contributes 10% of her salary before she pays taxes to a retirement account, and 25% of her remaining salary is then consumed in state and federal taxes, To determine what is Selena's annual intake home salary if she also has to pay $ 30 for health Insurance each month, the following calculation must be performed:
40,000 - (40,000 x 0.1) - (40,000 x 0.9 x 0.25) - (30 x 12) = X
40,000 - 4,000 - 9,000 - 360 = X
26.640 = X
Therefore, Selena's annual intake home salary is $ 26,640.
Find the arc length of the semicircle. Either enter an exact answer in terms of π or use 3.14 for π and enter your answer as a decimal.
Answer:
9.42
Step-by-step explanation:
The circumference of a circle is calculated using the following formula:
C=2πr (C: circumference, r : radius)
radius here is 6 and π is given as 3.14
2*(3.14)*6 = 18.84 now divide this by 2 to find the length of semicircle
18.84/2 = 9.42
Answer:
6π
Step-by-step explanation:
For the problem I thought it was asking about the lowest and greatest values. But that is incorrect therefore, my answer is wrong. How do I go about this problem then? How would I solve this?
You're right, this problem is asking for the least and greatest values. But, we have to take a bit of a closer look at the stem and leaf plot.
The left side is the ones place and the right side is the tenths place.
Using that information, the least data value is 2.5, and the greatest data value is 5.7.
Hope this helps!
