Answer:
7.88 x 10^5 is 788,000 is scientific notation
Which of the following are polynomials?
A. x^2 + x + 1/x^2 + 1
B. 2/x^3 + x + 1/2
C. 2/3x^2 + x + 1
D. x^2/3 + 0x + 1
E. x^3 + 2x + square root of 2
Answer: C, E
Step-by-step explanation:
These are polynomials by the definition of a polynomial.
compare the discounts you would receive with a 10% off coupon versus a 510 off coupon. Which one is better? Are there situations in which the other one is better? Will they get you the same amount of discount? Show All the work.
1. To determine the better option between a 10% off coupon versus a $10 off coupon, it is necessary to determine the coupon price.
2. On the other hand, the $10 off coupon becomes better when the coupon price is less than $100.
3. The 10% off coupon and the $10 off coupon do not give the same amount of discount unless the coupon or list price is $100 in both situations.
What is a discount?A discount is a monetary reduction in the cost of a good or service offered to customers to increase trade.
Offering discounts enhances sales but not profitability. So, there is a trade-off that must be considered properly.
Calculations:Ordinarily, if the coupon price is more than $100, the 10% off coupon becomes better than the $10 off coupon.
For instance, if the coupon price is $110, the 10% off coupon will yield a discount amount of $11 ($110 x 10%), which is more than $10.
For instance, if the coupon price is $99, the discount amount will be $9.90, which is less than $10.
Thus, a 10% off coupon and a $10 off coupon do not offer the same discount amount unless the list price is $100, no more, no less.
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Question Completion:Compare the discounts you would receive with a 10% off coupon versus a $10 off coupon.
What is the simplified form of i^86?
A. 1
B. i
C. -1
D. -i
1. Assuming that the company sells all that it produces, what is the profit function?
2. What is the domain of P(x) ?
3. The company can choose to produce either 50 or 60 items. What is their profit for each case, and which level of production should they choose? Profit when producing 50 items? Profit when producing 60 items?
4. Can you explain, from our model, why the company makes less profit when producing 10 more units?
The profit function is R(x) = -0.5 (x - 50²) + 1150
The domain of P(x) is: 0 ≤ x ≤ 150 Profit when producing 50 items = 1150 Profit when producing 60 items = 1100 What is the profit function about?Note that:
1. Profit = Revenue - cost
P (x) = 0.5 ( x - 90²) + 4050 - 40x - 100
= 0.5 ( x² - 180 + 8100 + 4050 - 40x - 100
=0.5 x² - 50x - 100
=0.5( x² - 100x) - 100
= -0.5 (x - 50²) + 1150
2. Since the minimum unit is 50.
Then x ≤ 150
X = describe the item so it need to be a negative number
x ≥ 0Hence the domain of P(x) is: 0 ≤ x ≤ 150
3. Assume x = 50 , 60
R(50) = 1150 , R (60 ) = -0.5 (60-50)² + 1150 = 1100
4. R (x) = -0.5 (x-50)² + 1150 then 50 more unit is removed hence, Profit when producing 60 items = 1100
Therefore, The profit function is R(x) = -0.5 (x - 50²) + 1150
The domain of P(x) is: 0 ≤ x ≤ 150 Profit when producing 50 items = 1150 Profit when producing 60 items = 1100Learn more about profit function from
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Fill in the missing amounts. July Aug. Sept. Oct. Nov. Dec. Receipts $500 $550 $700 $850 $795 $715 Expenses $490 $550 $600 $795 $ $650 Net Cash Flow $ $0 $ $55 $45 $ Cumulative Balance $10 $ $110 $ $210 $275
July Aug. Sept. Oct. Nov. Dec. Receipts $500 $550 $700 $850 $795 $715 Expenses $490 $550 $600 $795 $ $650 Net Cash Flow $ $0 $ $55 $45 $ Cumulative Balance $10 $ $110 $ $210 $275 the missing values are 750, 10, 100, 65, 10, 165
This is further explained below.
What is Cumulative Balance?Generally, The term "cumulative balance" refers to the total amount of money left over at the end of a fiscal year after all surplus amounts have been subtracted from deficit amounts. If there is a negative amount in the Cumulative Balance at the conclusion of a fiscal year, then that balance will be carried forward and used as the opening balance for the next fiscal year.
The term "cumulative account" refers to the total amount of an employee's account under a defined contribution plan (for an unaggregated plan) or the total amount of an employee's account under all defined contribution plans included in an Aggregation Group (for aggregated plans), both of which are determined as of the most recent plan valuation date within the most recent 12-month period that ends on the...
In conclusion, for the following data July Aug. Sept. Oct. Nov. Dec. Receipts $500 $550 $700 $850 $795 $715 Expenses $490 $550 $600 $795 $ $650 Net Cash Flow $ $0 $ $55 $45 $ Cumulative Balance $10 $ $110 $ $210 $275 the missing values are 750, 10, 100, 65, 10, 165
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2/3 of Ram money = 1/2 of Hari money. They have altogether 1400. Find the amount of money each.
Solving a system of equations we will see that Hari has 800 and Ram has 600.
How much money does each have?Let's define the variables:
R = money that Ram has.H = money that Hari has.We know that:
(2/3)*R = (1/2)*H
We also know that in total they have 1400, then:
R + H = 1400.
So we have the system of equations:
(2/3)*R = (1/2)*H
R + H = 1400.
In the first equation we can isolate R.
R = (3/2)*(1/2)*H = (3/4)*H
Now we can replace that in the other equation:
(3/4)*H + H =1400
H*(7/4) = 1400
H = (4/7)*1400 = 800
So Hari has 800, and:
R + H = 1400
R = 1400 - H = 1400 - 800 = 600
Hari has 800 and Ram has 600.
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In the circle below, O is the center and mGl= 145°. What is the measure of the central angle ZGOR? H G 0 145° I
The measure of the central angle is 290 degrees
How to determine the measure of the central angle?The measure of arc GI is given as:
mGI = 145 degrees
The measure of the central angle is calculated as:
Central angle = 2 * mGI
Substitute the known values in the above equation
Central angle = 2 * 145
Evaluate the product
Central angle = 290
Hence, the measure of the central angle is 290 degrees
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need heeeelp please
Answer: [tex]\Large\boxed{x=-\frac{4}{5} }[/tex]
Step-by-step explanation:
Given equation
[tex]-9+log_{4}(-5x)=-8[/tex]
Add 9 on both sides
[tex]-9+log_{4}(-5x)+9=-8+9[/tex]
[tex]log_{4}(-5x)=1[/tex]
Simplify the logarithm
[tex]-5x=4^1[/tex]
[tex]-5x=4[/tex]
Divide -5 on both sides
[tex]-5x\div-5=4\div-5[/tex]
[tex]\Large\boxed{x=-\frac{4}{5} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
(1 point) Find y as a function of x if
y" - 12y" + 32y' = 0,
y(0) = 5, y'(0) = 2, y" (0) = 1.
0
y(x) =
Question
Find the point-slope form of the equation of the line satisfying the given conditions and use this to write the slope-intercept form of the equation.
x-intercept - 5 and y-intercept = 4
Answer:
y=(−2)x−-6
Step-by-step explanation:
Use the slope −2 and the point (−5,4) to find the y-intercept.
y=mx+b
⇒4=(−2×−5)+b
⇒−4=10+b
⇒b=−6
Write the equation in slope intercept form as:
y=mx+b
⇒y=(−2)x−-6
0
100
200
300
400 500 600 700
Quantity Supplied
nstructions: Refer to the graph and answer the questions below.
Suppose the price is $6. What is the Quantity Supplied?
Suppose the Quantity Supplied is 200. What must the price be?
Suppose the price is $5 resulting in a Quantity Supplied of 300. Then the pric
Answer:
a. 400
b. 4$
Step-by-step explanation:
2$ equals 0 Quantity
3$ equals 100 Quantity
4$ equals 200 Quantity
We can see that starting from 2$, a dollar will increase the Quantity by 100
Teresa earns a weekly salary of $825 and a 6% commission on her total sales.
Ramón earns a weekly salary of $1,350 and a 2% commission on sales. What
amount of sales, x, will result in each of them earning the same amount for the
week?
To estimate the amount of sales, x, will result in each of them earning the same amount for the week and we can set up the following equation:
T = R
825 + 0.06x = 1350 + 0.02x
Simplifying the equation, we get
x = 13125
We require a total of 13125 for the number of sales to maintain the same amount for Ramon and Teresa at the end of the week.
How to estimate the number of sales, x, that will result in each of them gaining the exact amount for the week?
For this case, we can assume that the total salary for Teresa T is given by T = 825 + 0.06x
Where x represents the number of sales. And similarly the total salary of Ramon we have:
R = 1350 + 0.02x
We want to estimate the amount of sales, x, will result in each of them earning the same amount for the week and we can set up the following equation:
T= R
825 + 0.06x = 1350 + 0.02x
Multiply both sides by 100
[tex]$825 \cdot 100+0.06 x \cdot 100=1350 \cdot 100+0.02 x \cdot 100$[/tex]
82500 + 6x = 135000 + 2 x
Subtract 82500 from both sides
82500 + 6x - 82500 = 135000 + 2x - 82500
6x = 2x + 52500
Subtract 2x from both sides
6x - 2x = 2x + 52500 - 2x
4x = 52500
Divide both sides by 4
[tex]$\frac{4 x}{4}=\frac{52500}{4}$[/tex]
x = 13125
So then we require a total of 13125 for the number of sales to maintain the same amount for Ramon and Teresa at the end of the week.
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The large rectangle was reduced to create the small rectangle.
A large rectangle has a length of 18 inches and width of 12 inches. A smaller rectangle has a length of 6 inches and width of x inches.
Not drawn to scale
What is the missing measure on the small rectangle?
2 inches
3 inches
4 inches
5 inches
Answer:
4 inches
Step-by-step explanation:
large rectangle - 18:12 ratio = 3:2
small rectangle - 6:4 = 3:2
√₂º · Va This can be transformed into a basic integral by letting Consider the indefinite integral U= x' +9 ✓ and du = 7x6 ✓dx · √x + 9 dx: Performing the substitution yields the integral
Answer:
[tex]u = x^{7} +8[/tex] [tex]du = 7x^{6} dx[/tex] result is [tex]\frac{1}{7} \sqrt[4]{u}[/tex]
Step-by-step explanation:
Solve:
55) A pool is filling at 3 pts per min. How many gallons per hour is that?
Which of the following is the equation of the line that passes through the point (-5,-7) and has a slope of 2/5?
No multiple choice
The equation of the line passing through the point (-5, -7) with a slope of 2/5 is y = (2/5)x - 5.
How did we get the values?To find the equation of a line, we can use the point-slope form of a linear equation:
y - y₁ = m(x - x₁),
where (x₁, y₁) is the given point on the line and m is the slope.
In this case, the given point is (-5, -7) and the slope is 2/5. Substituting these values into the equation, we have:
y - (-7) = (2/5)(x - (-5)).
Simplifying further:
y + 7 = (2/5)(x + 5).
Distributing the 2/5:
y + 7 = (2/5)x + 2.
Subtracting 7 from both sides:
y = (2/5)x - 5.
Therefore, the equation of the line passing through the point (-5, -7) with a slope of 2/5 is y = (2/5)x - 5.
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A kite is flying 95 ft off the ground, and its string is pulled taut. The angle of elevation of the kite is 59 degrees. Find the length of the string. Round your answer to the nearest tenth.
If a kite is flying 95 ft. off the ground, and its string is pulled taut. The angle of elevation of the kite is 59 degrees. Then the length of the string will be 110.8 ft.
Given information constitutes the following,
The distance of the flying kite from the ground, length AB (refer the figure) = 95 ft.
The angle of elevation of the kite, ∠ACB = 59°
We have to find the length of the string, that is the length AC. For that, we can apply Trigonometry as shown in the next steps of the solution.
In ΔABC, as shown in the attached figure,
sin (∠ACB ) = AB / AC
⇒ sin (59°) = 95 / AC
0.8572 = 95 / AC
AC = 95 / 0.8572
AC = 110.814
AC ≈ 110.8 ft. [After rounding off to the nearest tenth]
Hence, the length of the string comes out to be 110.8 ft.
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s−3(s+6)= ASAP I NEED ANSWER PLEASE
Answer: −2(
Answer:
Simplified: −2s − 18
Step-by-step explanation:
Simplify the expression.
In the parallelogram below,
y = [? ]°
2
Z
1240
33%
Answer:
y = 33
Step-by-step explanation:
Angle y and 33 are alternate interior angles since the figure is a parallelogram and alternate interior angles are equal
y = 33
Answer:
y = 33°
Step-by-step explanation:
The diagonal of the parallelogram (a transversal) intersects two opposite and parallel sides of the parallelogram
Then
The angles of measures y° and 33° are Alternate interior angles
Then
they are congruent.
In other words , y = 33°
If 2/3x − 1 = 4, then x=
Answer: 15/2 or 7.5
Step-by-step explanation:
2/3x = 5
5 divided by 2/3 or 5 x 3/2
= 15/2 or 7.5
Answer: 15/2
Step-by-step explanation:
[tex]\frac{2}{3} x-1=4\\\\\frac{2}{3}x=5\\ \\x=5(\frac{3}{2})\\\\x=\frac{15}{2}[/tex]
Show that the function f(x)=sin3x + cos5x is periodic and it’s period.
The period of [tex]f(x)[/tex] is [tex]\boxed{2\pi}[/tex].
Recall that [tex]\sin(x)[/tex] and [tex]\cos(x)[/tex] both have periods of [tex]2\pi[/tex]. This means
[tex]\sin(x + 2\pi) = \sin(x)[/tex]
[tex]\cos(x + 2\pi) = \cos(x)[/tex]
Replacing [tex]x[/tex] with [tex]3x[/tex], we have
[tex]\sin(3x + 2\pi) = \sin\left(3 \left(x + \dfrac{2\pi}3\right)\right) = \sin(3x)[/tex]
In other words, if we change [tex]x[/tex] by some multiple of [tex]\frac{2\pi}3[/tex], we end up with the same output. So [tex]\sin(3x)[/tex] has period [tex]\frac{2\pi}3[/tex].
Similarly, [tex]\cos(5x)[/tex] has a period of [tex]\frac{2\pi}5[/tex],
[tex]\cos(5x + 2\pi) = \cos\left(5 \left(x + \dfrac{2\pi}5\right)\right) = \cos(5x)[/tex]
We want to find the period [tex]p[/tex] of [tex]f(x)[/tex], such that
[tex]f(x + p) = f(x)[/tex]
[tex] \implies \sin(3x + p) + \cos(5x + p) = \sin(3x) + \cos(5x)[/tex]
On the left side, we have
[tex]\sin(3x + p) = \sin(3x + 2\pi + p - 2\pi) \\\\ ~~~~~~~~ = \sin(3x+2\pi) \cos(p-2\pi) + \cos(3x+2\pi) \sin(p-2\pi) \\\\ ~~~~~~~~ = \sin(3x) \cos(p-2\pi) + \cos(3x) \sin(p - 2\pi)[/tex]
and
[tex]\cos(5x + p) = \cos(5x + 2\pi + p - 2\pi) \\\\ ~~~~~~~~ = \cos(5x+2\pi) \cos(p-2\pi) - \sin(5x+2\pi) \sin(p-2\pi) \\\\ ~~~~~~~~ = \cos(5x) \cos(p-2\pi) - \sin(5x) \sin(p-2\pi)[/tex]
So, in terms of its period, we have
[tex]f(x) = \sin(3x) \cos(p - 2\pi) + \cos(3x) \sin(p - 2\pi) \\\\ ~~~~~~~~ ~~~~+ \cos(5x) \cos(p - 2\pi) - \sin(5x) \sin(p - 2\pi)[/tex]
and we need to find the smallest positive [tex]p[/tex] such that
[tex]\begin{cases} \cos(p - 2\pi) = 1 \\ \sin(p - 2\pi) = 0 \end{cases}[/tex]
which points to [tex]p=2\pi[/tex], since
[tex]\cos(2\pi-2\pi) = \cos(0) = 1[/tex]
[tex]\sin(2\pi - 2\pi) = \sin(0) = 0[/tex]
Will mark brainliest
[tex]x^3[/tex] is strictly increasing on [0, 5], so
[tex]\max\{x^3 \mid 0\le x\le5\} = 5^3 = 125[/tex]
and
[tex]\min\{x^3 \mid 0 \le x\le5\} = 0^3 = 0[/tex]
so the integral is bounded between
[tex]\displaystyle \boxed{0} \le \int_0^5x^3\,dx \le \boxed{125}[/tex]
Solve the inequality
21≥t+10
The answer is t ≤ 11.
Subtract 10 from each side.21 - 10 ≥ t + 10 - 10t ≤ 11evaluate the following using powers of ten rules: 10 to the 4th times the square root of 1.042
The value of the given expression is approximate equal to 1.021 × 10⁴ OR 10207.8
Evaluating an expressionFrom the question, we are to determine the value of the given expression
The given expression is
10 to the 4th times the square root of 1.042
That is,
10⁴ × √1.042
The expression can be evaluated as shown below
10⁴ × √1.042
= 10⁴ × 1.02078
= 1.02078 × 10⁴
≈ 1.021 × 10⁴
OR
= 1.02078 × 10⁴ = 10207.8
Hence, the value of the given expression is approximate equal to 1.021 × 10⁴ OR 10207.8
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2) Find the perimeter and area of the figures:
a)
P =
A =
8
8 ft.
b)
P =
A =
12
5m
Answer:
8+8+12+5= 33
Step-by-step explanation:
8+8+12+5=33
4 1/3 - 1 2/3 how to solve this please
Answer:
[tex]2\frac{2}{3}[/tex]
Step-by-step explanation:
1) Convert [tex]4\frac{1}{3}[/tex] to improper fraction. Use this rule: [tex]a\frac{b}{c} =\frac{ac+b}{c}[/tex].
[tex]\frac{4\times3+1}{3} -1\frac{2}{3}[/tex]
2) Simplify 4 * 3 to 12.
[tex]\frac{12+1}{3}[/tex]
3) Simplify 12 + 1 to 13.
[tex]\frac{13}{3} -1\frac{2}{3}[/tex]
4) Convert [tex]1\frac{2}{3}[/tex] to improper fraction. Use this rule: [tex]a\frac{b}{c} =\frac{ac+b}{c}[/tex].
[tex]\frac{13}{3} -\frac{1\times3+2}{3}[/tex]
5) Simplify 1 * 3 to 3.
[tex]\frac{13}{3} -\frac{3+2}{3}[/tex]
6) Simplify 3 + 2 to 5.
[tex]\frac{13}{3} -\frac{5}{3}[/tex]
7) Join the denominators.
[tex]\frac{13-5}{3}[/tex]
8) Simplify.
[tex]\frac{8}{3}[/tex]
9) Convert to mixed fraction.
[tex]2\frac{2}{3}[/tex]
(Decimal Form: 2.666667)
Thank you,
Eddie
P: 2,012
1) El volumen de un cubo de arista 1 es Vc = 1³ y el
Volumen de una esfera de radior es
JE
V₁ = πr ²³ Entonces si en un cubo de arista 4cm
3
y se introduce una pelota de diametro 4 cm, al Calcular
aproximación con cuatro cifras decimales, por exceso.
Calcular el volumen que queda entre la esfera y el cubo.
(toma π =
3,141592654)
El volumen remanente entre la esfera y el cubo es igual a 30.4897 centímetros cúbicos.
¿Cuál es el volumen remanente entre una caja cúbica vacía y una pelota?
En esta pregunta debemos encontrar el volumen remanente entre el espacio de una caja cúbica y una esfera introducida en el elemento anterior. El volumen remanente es igual a sustraer el volumen de la pelota del volumen de la caja.
Primero, se calcula los volúmenes del cubo y la esfera mediante las ecuaciones geométricas correspondientes:
Cubo
V = l³
V = (4 cm)³
V = 64 cm³
Esfera
V' = (4π / 3) · R³
V' = (4π / 3) · (2 cm)³
V' ≈ 33.5103 cm³
Segundo, determinamos la diferencia de volumen entre los dos elementos:
V'' = V - V'
V'' = 64 cm³ - 33.5103 cm³
V'' = 30.4897 cm³
El volumen remanente entre la esfera y el cubo es igual a 30.4897 centímetros cúbicos.
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After descending 8.25 feet, a bird is now
at a height of 16.5 feet. What was the initial
height of the bird?
A student says that 3% is equal to 0.3 when written as a decimal. Is their thinking correct? Explain.
The answer is no.
Always remember when converting from percent to decimal, divide by 100%.
3% ÷ 100%0.03 ≠ 0.3Hence, the student's thinking is not correct.
Answer:
no
Step-by-step explanation:
0.3 = 30% not 3%
to change a percentage to a decimal fraction, divide by 100
3% = [tex]\frac{3}{100}[/tex] = 0.03
The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 39 ounces and a standard deviation of 5 ounces.
Use the Standard Deviation Rule, also known as the Empirical Rule.
Suggestion: sketch the distribution in order to answer these questions.
The answer to these questions are
Option A: This is in the attachmentOption B : 24 and 54Option C: 97.59%Option D: 84.13%
How to find the point where the distribution lies at 99.7%. The data is 3 sd from mean
Hence
39 - 3*(5) = 24
39 + 3*(5) = 54
The widget lies between 24 and 54
c. P(29.0 < x < 54.0)
= 29 - 39 / 5 and 54 - 39 / 5
= -2.0 and 3.0
We have to find P(Z < 3.0) - P(Z < -2.0)
= 0.9987 - 0.0228
= 97.59%
d. x = 44
= 44 - 39/ 5
= 1
We are to find P(z < 1.0) = 84.13%
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