The " Eight further than the Quotient of a number and 7 is equal to 3," and the result to the equation is x = -35.
The equation 8( x/ 7) = 3 represents the judgment " Eight further than the Quotient of a number and 7 is equal to 3," and the result to the equation is x = -35.
" Eight further than" implies addition, so we've 8 " The quotient of a number and 7" means dividing a number by 7, so we've x/ 7 " is equal to" means that the expression on the left side is equal to the expression on the right side, so we've = " 3" is the value to which the expression on the left side is equal, so we've 3 Putting it all together the judgment " Eight further than the quotient of a number and 7 is equal to 3" can be restated into the equation ( x/ 7) = 3
In this equation, x represents the number we're trying to find. To break for x, we can manipulate the equation using algebraic operations to insulate x on one side of the equation. By abating 8 from both sides of the equation, we get ( x/ 7)- 8 = 3- 8 Simplifying, we have x/ 7 = -5
To insulate x, we can multiply both sides of the equation by 7 *( x/ 7) = -5 * 7 This gives us x = -35 thus, the equation 8( x/ 7) = 3 represents the judgment " Eight further than the quotient of a number and 7 is equal to 3," and the result to the equation is x = -35.
To know more about Quotient .
https://brainly.com/question/11418015
#SPJ11
Which of these expressions is equivalent to 2/0.4? (Iready)
Answer:
5
-----
0.4 | 2
- 0
2.0
- 1.6
-----
4
What is the diameter of a sphere with a volume of 79cm^3, to the nearest tenth of a centimeter?
The diameter of the sphere to the nearest tenth is [tex]5.3\ cm[/tex].
According to the question:
[tex]Volume(V) = 79\ cm^3[/tex]
To find:
[tex]Radius(r)[/tex]
We know that:
[tex]V = \frac{4}{3}\pi r^3[/tex]
⇒ [tex]r = (\frac{3V}{4\pi})^{1/3}[/tex]
Take [tex]\pi[/tex] = [tex]3.1415[/tex] and substitute the given values in the above equation:
[tex]r = (\frac{3\times 79}{4\times 3.1415})^{1/3}[/tex] ...(∵ [tex]\pi = 3.1415[/tex])
[tex]r = 18.8604^{1/3}[/tex]
[tex]r = 2.661\ cm[/tex]
⇒[tex]diameter = 2\times 2.661\ cm[/tex]
⇒[tex]diameter = 5.322\ cm[/tex]
Rounded to the nearest tenth:
[tex]diameter = 5.3\ cm[/tex]
Therefore, the diameter of the sphere to the nearest tenth is [tex]5.3\ cm[/tex].
Read more about spheres here:
https://brainly.com/question/30522100
Please help. Use the alternative form of definition of derivative to find the slope of the line tangent. Please show work. 100 points. Will give brainliest, when it comes up.
The slope of the line tangent to the graph of h(x) = 1/x + 3 at the point when x is -6 is -1/36.
What is the slope of the line tangent to the equation?To determine the slope of the line tangent to the graph of the given function when x = -6;
Using alternative form of the definition of derivative.
f'(a) = lim (h->0) [f(a+h) - f(a)] / h
Using this formula for the given function;
h'(a) = lim (h->0) [h(a+h) - h(a)] / h
Now, substitute a = -6 into the formula:
h'(-6) = lim (h->0) [h(-6+h) - h(-6)] / h
Next, simplify the expression by plugging in the values:
h'(-6) = lim (h->0) [1/(-6+h) + 3 - (1/-6 + 3)] / h
Simplifying further:
h'(-6) = lim (h->0) [1/(-6+h) - 1/-6] / h
Now, let's combine the fractions with a common denominator:
h'(-6) = lim (h->0) [(-6 - (-6+h))/((-6+h)(-6))] / h
Simplifying the numerator:
h'(-6) = lim (h->0) [-h / ((-6+h)(-6))] / h
Canceling out the h's:
h'(-6) = lim (h->0) [-1 / ((-6+h)(-6))]
Taking the limit as h approaches 0:
h'(-6) = -1 / ((-6)(-6))
Simplifying further:
h'(-6) = -1 / 36
Learn more on slope of line tangent here;
https://brainly.com/question/6353432
#SPJ1
Please help!
find the ending size or value for the tenth or tenth of a percent.
given percent change.
a. A $100 stock loses 20% of its value.
b. An $80 stock gains 20% of its value.
Answer: a. A $100 stock loses 20% of its value.
To find the ending value of the stock after a 20% decrease in value, we can multiply the initial value by (1 - 0.20) or 0.80.
Ending value = $100 x 0.80 = $80
Therefore, the ending value of the stock after a 20% decrease is $80.
b. An $80 stock gains 20% of its value.
To find the ending value of the stock after a 20% increase in value, we can multiply the initial value by (1 + 0.20) or 1.20.
Ending value = $80 x 1.20 = $96
Therefore, the ending value of the stock after a 20% increase is $96.
Step-by-step explanation: :)
If cards are sold at the rate of 3 for 10c,what will be the costof 3-dozen such cards?
Answer:
120c
Step-by-step explanation:
3 for 10c 1 for 10/3c 3*12 for 10/3 *36 =12*10=120c is the cost of 3 dozen of such cards
Written in simple form
Answer:
a = 8, b = 2
Step-by-step explanation:
[tex]\sqrt[3]{x^{10} }[/tex] ( substitute x = - 2
= [tex]\sqrt[3]{(-2)^{10} }[/tex]
= [tex]\sqrt[3]{1024}[/tex]
= [tex]\sqrt[3]{2^{10} }[/tex]
= [tex]\sqrt[3]{2^{9 (2)} }[/tex]
= 2³ [tex]\sqrt[3]{2}[/tex]
= 8[tex]\sqrt[3]{2}[/tex] ← in the form a[tex]\sqrt[3]{b}[/tex]
with a = 8 and b = 2
a study of long-distance phone calls made from general electric reveled the length of the calls, in minutes, follows the normal probability distribution. the mean length of time per call was 4.5 minutes and the standard deviation was 0.70 minutes. what is the probability that calls last between 4.0 and 6.0 minutes?
The probability that calls last between 4.0 and 4.6 minutes will be around 0.4332.
we have to standardize the values and utilize the standard typical dispersion table or calculator.
To discover the z-scores for 4.0 and 6.0 minutes:
z1 = (4.0 - 6.0 ) / 0.70 = 2.8
z2 = (4.5 - 6.0 ) / 0.70= 2.1
Since Employing a standard ordinary conveyance table, we are able to discover the likelihood of the calls enduring between 4.0 and 4.6 minutes:
P(0 ≤ Z ≤ 2.1) = 0.4332
However the likelihood that calls final between 4.0 and 4.6 minutes is 0.4332, or around 0.4332.
To know more about probability refer to this :
brainly.com/question/24756209
#SPJ1
Determine the equation of the parabola that opens to the right, has focus (13,-6),
and a focal diameter of 28.
The equation of the parabola is[tex](y + 6)^2 = 4(x - 13)[/tex], where the vertex is (13, -6) and the distance between the directrix and focus is 14.
To determine the equation of the parabola, we need to use the standard form for a parabola with a horizontal axis:
[tex](x - h)^2 = 4p(y - k)[/tex]
Where (h, k) represents the vertex of the parabola, and p is the distance from the vertex to the focus (and also from the vertex to the directrix).
Given that the parabola opens to the right, the vertex will be on the left side. Let's assume the vertex is (h, k).
We know that the focus of the parabola is at (13, -6), so the distance from the vertex to the focus is p = 13 - h.
We are also given that the focal diameter is 28, which means the distance between the directrix and the focus is twice the distance from the vertex to the focus.
Therefore, the distance from the vertex to the directrix is d = 28/2 = 14.
for such more question on parabola
https://brainly.com/question/18274774
#SPJ11
A simulated game of chess is programmed between two computers. The game is supposed to be biased in favor of player B winning 4 out of 5 times. Which is the most suspicious set of outcomes of 30 games played between the two computers?
A.
AABABBBABBBBBBBBABBBABBBBBBBBA
B.
ABBABBAABBBBBABBBBBBBBBBBBBABB
C.
ABBABABABABBABABABABABABABABAA
D.
ABBABBBABBBBBBBBABBBABBBBBBBBB
The most suspicious set of outcomes of 30 games played between the two computers would be option C: ABBABABABABBABABABABABABABABAA.
In a fair game where player B is supposed to win 4 out of 5 times, we would expect player B to win approximately 24 out of 30 games. However, option C shows player B winning only 6 out of 30 games, which deviates significantly from the expected outcome.
This set of outcomes suggests a strong bias towards player A winning, as player B's wins are significantly lower than expected.
It is highly unlikely to observe such a low success rate for player B if the game was truly biased in favor of player B winning 4 out of 5 times.
Option C raises suspicions of an unfair advantage given to player A, potentially indicating some manipulation or incorrect implementation in the programming of the game.
Further investigation would be warranted to determine the cause of this biased outcome and to ensure fair play between the two computers in future games.
For similar question on outcomes.
https://brainly.com/question/12342341
#SPJ11
A cone-shaped paperweight is 5 inches tall, and the base has a circumference of about 12.56 inches. What is the area of a vertical cross section through the center of the base of the paperweight? Use 3.14 for π .
The area of the vertical cross section through the center of the base of the paperweight is approximately 12.56 square inches.
To find the area of a vertical cross section through the center of the base of the cone-shaped paperweight, we need to determine the radius of the base first.
The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. In this case, we know the circumference is about 12.56 inches, so we can set up the equation:
12.56 = 2πr
To solve for r, we divide both sides of the equation by 2π:
r = 12.56 / (2π)
Now we can calculate the radius:
r ≈ 12.56 / (2 × 3.14)
r ≈ 12.56 / 6.28
r ≈ 2 inches
The radius of the base is approximately 2 inches.
Since the vertical cross section passes through the center of the base, the shape of the cross section is a circle. The formula for the area of a circle is A = [tex]πr^2[/tex], where A is the area and r is the radius.
Now we can calculate the area of the cross section:
A = [tex]πr^2[/tex]
A ≈ 3.14 × [tex](2^2)[/tex]
A ≈ 3.14 × 4
A ≈ 12.56 square inches
Therefore, the area of the vertical cross section through the center of the base of the paperweight is approximately 12.56 square inches.
For such more questions on Cone Cross Section Area
https://brainly.com/question/29140252
#SPJ11
Draw a graph of y=log_1/3 (x) and its inverse on the same pair of axis.
The graph of y = log1/3(x) is a decreasing curve that passes through the points (1, 0) and (3, -1). The horizontal asymptote is y = 0, and the vertical asymptote is x = 0.
The inverse of y = log1/3(x) is x = 3^y, which is equivalent to y = log3(x). The graph of y = log3(x) is an increasing curve that passes through the points (1, 0) and (3, 1). The horizontal asymptote is y = 0, and the vertical asymptote is x = 0.
When both graphs are plotted on the same pair of axis, they intersect at the point (1, 0) and (3, -1) and (3, 1).
Step tariffs 0-6 ke 7-15 ke 16-30 ke 31-60 ke Above 61 ke Basic charge per month 2016/2017 Prices (R) per 6,91 15,95 17,00 19, 04 21,58 22,00 % increase 8% 9% 11% 11,5% 12,5% 12% 2017/2018 Prices (R) per 7,46 17,39 Use the table above to answer the questions that follow 2.1.1 Define the basic charge in the given context. 2.1.2 Show how the tariff of R18,87 during 2017/2018 was calculated. 18,87 21,23 24, 28 24, 64 2.1.3 Mr Morake's municipal bill showed R201,27, for water usage at the end of August 2018. He stated that the basic charge was not included on the water bill. Verify if this statement is correct. (2) (2)
2.1.1: The basic charge in the given context refers to a fixed monthly fee that is charged by the municipality for the provision of water services, regardless of the amount of water consumed by the user.
2.1.2: To calculate the tariff for a particular consumption level during 2017/2018, you need to find the relevant consumption tier and then apply the corresponding rate. For example, if the consumption level is 10,000 litres per month, then the relevant tier is 7-15 kilolitres, and the rate for this tier is R15.95 per kilolitre. Therefore, the cost of water for this consumption level is:
10 kilolitres x R15.95/kilolitre = R159.50
To this cost, the basic charge needs to be added. According to the table, the basic charge for 2017/2018 is R7.46 per month. Therefore, the total cost of water and basic charge for this consumption level is:
R159.50 + R7.46 = R166.96
Therefore, the tariff for a consumption level of 10,000 litres per month during 2017/2018 is R166.96.
2.1.3: To verify if Mr Morake's statement is correct, we need to check if the basic charge was included in the calculation of his water bill. Assuming that Mr Morake's water usage for the month of August 2018 fell within the 7-15 kilolitre tier, we can calculate his bill as follows:
Water usage: 10 kilolitres
Cost of water: 10 kilolitres x R17.39/kilolitre = R173.90
Based on the above calculation, it appears that the basic charge was included in Mr Morake's water bill, as his total bill of R201.27 exceeds the cost of water alone. Therefore, it seems that Mr Morake's statement is incorrect, and the basic charge was indeed included in his water bill.
1. The demand of calculators when its price per unit is Rs 1200,is Rs 4000. When the price increases to Rs 1500, only 3000 calculators are demanded. a.Find the demand equation in the form of p = f(Q) b.Obtain the number of calculations demanded when the price per unit calculators is Rs 1650 c. If 4500 calculations are demanded, what should be the price per unit of calculator?
a. The demand equation is p=−300Q+6000.
b. When the price per unit is Rs 1650, the number of calculators demanded is 2500.
c. When 4500 calculators are demanded, the price per unit is Rs 900.
How to calculate the valuea. The slope of the demand curve is m = 0.3. We can find the y-intercept by substituting the slope and one of the points into the demand equation. When the price is Rs 1200, the quantity demanded is 4000. Therefore, the y-intercept is b=1200−(−0.3)(4000)=2400.
The demand equation is p=−0.3Q+2400.
1650 = 0.3Q - 2400
b. When the price per unit is Rs 1650, the number of calculators demanded is:
= (1650 - 2400) /-0.3
= 2500.
c. To find the price per unit of calculator when 4500 calculators are demanded, we substitute Q = 4500 into the demand equation and solve for p:
p = 0.3(4500) + 2400
p = 900
Learn more about equations on
https://brainly.com/question/2972832
#SPJ1
1 Choose the correct answer : 1 If 6* = 7, then 6 x+1 = *****.
The value of 6(x + 1), given that 6* = 7 is [tex](7/6)x + 7/6.[/tex]
What is the value if 6* equals 7?Given that 6* equals 7, we will solve for the value of "" by dividing 7 by 6.
6 = 7
= 7/6
To get value of 6 multiplied by (x + 1), we substitute the value of "*" into the expression:
6 * (x + 1) = (7/6) * (x + 1)
Expanding expression:
6 * (x + 1) = 7/6 * x + 7/6 * 1
6 * (x + 1) = 7/6 * x + 7/6
Read more about expression
brainly.com/question/1859113
#SPJ1
twenty-nine percent of all light emitting diode displays are manufactured by samsung. what is the probability that in a collection of two independent purchases, at lease one is a sumsung?
Answer:
The probability that at least one of two independent purchases is a Samsung display can be calculated using the complement rule:
P(at least one Samsung) = 1 - P(neither is a Samsung)
The probability that neither of the two purchases is a Samsung display is:
P(neither is a Samsung) = (1 - 0.29) x (1 - 0.29) = 0.51
Therefore, the probability that at least one of the two purchases is a Samsung display is:
P(at least one Samsung) = 1 - 0.51 = 0.49
The probability that in a collection of two independent purchases, at least one is a Samsung is 0.49.
A wheelchair ramp is 4.2m long. It rises 0.7m what is its angle of inclination to the nearest degree? Solve step by step
Sure, I can help you solve that math problem step by step.
First, we need to find the length of the hypotenuse of the ramp using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides (a^2 + b^2 = c^2).
So, using that formula, we can calculate the length of the ramp's hypotenuse: c^2 = 4.2^2 + 0.7^2
c^2 = 17.64 + 0.49
c^2 = 18.13
c = sqrt(18.13)
c = 4.26m
Now that we have the length of the hypotenuse, we can use the inverse trigonometric function of sine to find the angle of inclination. The sine of an angle is equal to the opposite side (in this case, the rise of the ramp, which is 0.7m) over the hypotenuse (4.26m).
So, sin(theta) = opposite/hypotenuse
sin(theta) = 0.7/4.26
sin(theta) = 0.1643
Now, we need to find theta by taking the inverse sine of 0.1643 (or sin(theta)).
theta = sin^-1(0.1643)
theta = 9.47 degrees
So the angle of inclination of the ramp to the nearest degree is 9 degrees.
Question 8 (2 points) Saved
What are the ways to determine if a relation is a function? Select EACH correct
answer.
Passes a horizontal line test.
Passes vertical line test.
No repeating x values,
No repeating y values.
Answer: passes a horizontal AND vertical line test✅; no repeating x values✅
Step-by-step explanation:
To pass a line test, the function must pass BOTH the horizontal and vertical line test. If it only passes one but not the other, is it NOT a function.
Lastly, it can be a function if it has repeating y values.
look at the image below 5 6 7
Answer:
30
Step-by-step explanation:
We can move the triangle on the top to the bottom to form a rectangle.
Then, it is 5x6 = 30.
In the figure below, points D, E, and F are the midpoints of the sides of ΔABC
Suppose AB = 48, BC = 56, and DE = 32.
Find the following lengths
The values of
1. DF = 28cm
2. AC = 64 cm
3. CF = 32 cm
What is segment theorem?It states that the line segment in a triangle joining the segment of any two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”
Therefore we can say that;
triangles , BDE, AD ,EFC, DE are congruent.
congruent triangles are triangles with equal sides and equal angles.
D = BE
BE = 56/2 = 28cm
A = DE = 32 cm
AC = 2AF
= 2 × 32 = 64 cm
learn more about segment theorem from
https://brainly.com/question/28667736
#SPJ1
the median of a given data set is also the
solve the following proportion
Answer: 4.5 or A
Step-by-step explanation:
1) Find LCM of 9 and 6, which is 18.
2) Multiply x/9 by 2. (2x/18)
3) Multiply 3/6 by 3. (9/18)
4) Divide by 2 (numberator on both sides)
x = 4.5
help its due tomorrow
Answer:
c) The equation of this line is y = 3x + 12.
Which expression is equivalent to
3xy-3
15x2,10?
2,10? Assume X*0,y*0
The expression which is equivalent to the given expression is 1 / 5x⁸ y¹³.
Given expression is,
3 x⁻⁶y⁻³ / 15 x² y¹⁰
We have to find the equivalent expression for this, which means that the end value for both expressions will be same.
We can write the given expression as,
3/15 × (x⁻⁶ / x²) × (y⁻³ / y¹⁰)
1/5 × (x⁻⁶ ⁻ ²) × (y⁻³ ⁻ ¹⁰)
= x⁻⁸ y⁻¹³ / 5
When the variables goes in to the denominator sign changes to positive in the exponent.
= 1 / 5x⁸ y¹³
Hence the correct expression is 1 / 5x⁸ y¹³.
Learn more about Equivalent Expressions here :
https://brainly.com/question/28170201
#SPJ1
Does 17 divide each of these numbers?
a)68 b) 84 c) 357 d) 1001
Hello !
68/17 = 4
=> yes for 68
84/17 = 4.941...
=> no for 84
357/17 = 21
=> yes for 357
1001/17 = 58.882...
=> no for 1001
Solve the inequality.
Created with Rapha�l 2.1.2
-
9.
5
+
6
x
≥
4
2.
1
Apply properties:
Add
Subtract
Multiply
Divide
To start over:
Reset
To solve the inequality:
9.5 + 6x ≥ 42.1
We will follow these steps:
Subtract 9.5 from both sides of the inequality:
9.5 + 6x - 9.5 ≥ 42.1 - 9.5
6x ≥ 32.6
Divide both sides of the inequality by 6:
(6x) / 6 ≥ 32.6 / 6
x ≥ 5.433333...
Rounded to two decimal places, the solution to the inequality is:
x ≥ 5.43
Lamar rented a truck for one day. There was a base fee of $16.95, and there was an additional charge of 74 cents for each mile driven. Lamar had to pay $155.33 when he returned the truck. For how many miles did he drive the truck?
Answer:187 miles
Step-by-step explanation: 155.33-16.95=138.38/74=187
5 The population of a country was 13.1 million. (a) Nine hundred thousand of the population were at least 2 metres tall. How many were less than 2 metres tall?
PLS HELP ASAP I NEED IT PLS
Step-by-step explanation:
The equation for this function is y=2x
So 32*2=64
36/2=18
2*x=2x
y/2=y/2
2x*2=4x
(x+3)*2=2x+6
Estimate the sum of the weights of Frailyn 10.2 pounds +611/12 pounds. Which statements are true about the estimate CHECK ALL THAT APPLY
2) A loan application was received and processed at Boyz Credit Union. A rate of 14% was indicated. At the end of the first year the borrower paid an interest on the loan of $1680.00. What was the amount borrowed?
Step-by-step explanation:
14÷100×1680.00
=$235,20