Answer: y = 5.4
Step-by-step explanation: This is a proportional statement. So we can set up a system of proportions.
So we know when x is 5, y is 3. Thus, we can set up a proportion [tex]\frac{x}{y}[/tex] such that substituting will give [tex]\frac{5}{3}[/tex].
Now, we know when x is 9, y is some unknown number. So we can set up the second proportion as [tex]\frac{9}{y}[/tex].
Since 5/3 and 9/y are directly proportional, these 2 expressions are therefore equal. So we have [tex]\frac{5}3}[/tex] [tex]= \frac{9}{y}[/tex].
Cross multiplying, we get [tex]5y = 27[/tex].
Dividing by 5, we get [tex]y = 5.4[/tex]
Hope this helped!
Please select the best answer from the choices provided .
Answer: B: (1-5x²)³, all real numbers
Step-by-step explanation:
The notation [tex]f\circ g(x)[/tex] is called function composition, which is where you pass one function in as the value of another function. In other words, [tex]\( f\circ g(x)=f(g(x)) \)[/tex].
Since we have the values for f(x) and g(x), let's plug them in.
[tex]f(g(x))\\f(1-5x^2)\\(1-5x^2)^3[/tex]
Hence, the best answer choice is B, as all real numbers would work and it is the cube of 1 - 5x².
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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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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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
evaluate 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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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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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]
1. a) Sajina deposited Rs 20,000 at the rate of 8% p.a. in her saving account. After 2 years, she withdrew Rs 5,000 and the total interest of 2 years. How long should she keep the remaining amount to get total interest of Rs 6,800 from the beginning?
6,800 to get a total interest of Rs 6,800 and keep the balance for 3 years.
What is meant by total interest?Total interest is the sum of all interest payments made during the course of an account or loan, including compounded amounts on accumulated interest that has not yet been paid.The equation [Total Loan Amount] = [Principle] + [Interest Paid] + [Interest on Unpaid Interest] can be used to calculate it.Under Section 24, you may deduct up to Rs 2 lakh from your total income for the interest component of the EMI you paid during the year.
How long should she keep the remaining amount to get a total interest of Rs 6,800 from the beginning:
The rate of 8% p.a. in her saving account.
20,000 at 8% interest for 2 years:
= 20,000*2*8/100
= 3200
5000 was withdrawn after 2 years and earned interest.
After 2 years, the new principal:
= 20000- 5000
=15000
She needs to get interested of 6800–3200 =3600 for the next N years.
N= 100* I /PR
= 100*3600/(15000*8)
=3
6,800 to get a total interest of Rs 6,800 and keep the balance for 3 years.
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Sajina should keep the remaining amount for 3 years to get a total interest of Rs 6,800 from the beginning.
What is the formula for total interest?For the principal [tex]P[/tex] and the rate of interest [tex]r\%[/tex] per annum, the total interest after [tex]t[/tex] years is given by the formula: [tex]I=\dfrac{Prt}{100}[/tex].
Given that Sajina deposited Rs 20,000 at the rate of 8% p.a. in her savings account.
So, [tex]P=20,000[/tex] and [tex]r=8[/tex].
Thus, after t=2 years the total interest would be
[tex]I=\dfrac{Prt}{100}\\\Longrightarrow I=\dfrac{20000\times 8\times 2}{100}\\\therefore I=3200[/tex]
So, the total interest after 2 years would be Rs 3,200.
Given that Sajina withdrew Rs 5,000 and the total interest of 2 years.
So, the new principal will be [tex]P'=20,000-5,000=\test{Rs}\hspace{1mm}15,000[/tex].
The total interest she wanted to gain is Rs 6,800. She had already gained Rs 3,200.
so, the remaining interest [tex]I'=6,800-3,200=\text{Rs}\hspace{1mm}3,600[/tex].
Let the required time be [tex]t'[/tex] years after how many years she got a total interest of Rs 6,800 from the beginning.
For principal [tex]P'=15,000[/tex], rate of interest [tex]r=8\%[/tex]; the total interest after [tex]t'[/tex] years would be [tex]I'=\dfrac{P'rt'}{100}=\dfrac{15000\times 8\times t'}{100}=1200t'[/tex]. But given that [tex]I'=3600[/tex].
So, we must have
[tex]1200t'=3600\\\Longrightarrow t'=\dfrac{3600}{1200}\\\therefore t'=3[/tex]
Therefore, Sajina should keep the remaining amount for 3 years to get a total interest of Rs 6,800 from the beginning.
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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.
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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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]
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
What is the simplified form of i^86?
A. 1
B. i
C. -1
D. -i
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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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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(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) =
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.
Please help me with this question <3
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
For two lines to be parallel, there should be angles that follow some specific properties that is usually observed with parallel lines.
We can clearly see that :
[tex] \qquad❖ \: \sf \: \angle7 \cong \angle16[/tex]
( by Alternate interior angle pair )
[tex] \qquad \large \sf {Conclusion} : [/tex]
Lines l and m are parallel to each other.
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
√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:
s−3(s+6)= ASAP I NEED ANSWER PLEASE
Answer: −2(
Answer:
Simplified: −2s − 18
Step-by-step explanation:
Simplify the expression.
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]
A baseball travels d meters t seconds after being dropped from the top of the building
Considering the given function, it is found that:
When t = 0, d = 0 meters.When t = 0.5, d = 1.25 meters.When t = 1, d = 5 meters.When t = 1.5, d = 11.25 meters.When t = 2, d = 20 meters.Since the changes for each 5 second interval are not the same, the ball is not traveling at a constant speed.
What is the function for the distance traveled by the ball?The function is:
d = 5t².
Hence:
When t = 0, d = 5 x 0² = 0 meters.When t = 0.5, d = 5 x 0.5² = 1.25 meters.When t = 1, d = 5 x 1 = 5 meters.When t = 1.5, d = 5 x 1.5² = 11.25 meters.When t = 2, d = 5 x 2² = 20 meters.Since the changes for each 5 second interval are not the same, the ball is not traveling at a constant speed.
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please help urgently
Answer: no real solution
Thus, the function has no x- intercept
Step-by-step explanation:
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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Solve the inequality
21≥t+10
The answer is t ≤ 11.
Subtract 10 from each side.21 - 10 ≥ t + 10 - 10t ≤ 11
Solve:
55) A pool is filling at 3 pts per min. How many gallons per hour is that?
After descending 8.25 feet, a bird is now
at a height of 16.5 feet. What was the initial
height of the bird?
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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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