Answer:
x = 1.3472 to the nearest ten thousandth.
Step-by-step explanation:
14^x + 1 = 36
14^x = 35
Taking logarithms:-
x ln 14 = ln 35
x = ln 35 / ln 14
= 1.3472.
The solution, rounded to the nearest ten-thousandth, is x = 1.5404.
To solve the equation [tex]14^x + 1 = 36[/tex], we first isolate the exponential term by subtracting 1 from both sides of the equation, which gives us [tex]14^x = 35.[/tex]
The next step is to take the logarithm of both sides of the equation.
We could use any base for the logarithm, but it's common to use base 10 or the natural logarithm base (e). In this case, let's use the natural logarithm:
[tex]ln(14^x) = ln(35)[/tex]
We can then use the property of logarithms which allows us to bring the exponent down as a multiplier:
[tex]x * times ln(14) = ln(35)[/tex]
Now, you can solve for x by dividing both sides by ln(14):
[tex]x = ln(35) / ln(14)[/tex]
Using a calculator, we find the quotient and then round to the nearest ten-thousandth:
x = 1.5404
This value is the solution to the original equation.
please help me with these questions
3. Answer: y = 4
Step-by-step explanation:
Need to find the slope (m):
[tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\dfrac{4 - 4}{-3-1}[/tex]
= [tex]\dfrac{0}{-4}[/tex]
= 0
Now input ONE of the points (1, 4) and the slope (m = 0) into the Point-Slope formula:
y - y₁ = m(x - x₁)
y - 4 = 0(x - 1)
y - 4 = 0
y = 4
********************************************************************
4. Answer: [tex]\bold{y = \dfrac{2}{3}x + 3}[/tex]
Step-by-step explanation:
[tex]y - y_1 = m(x - x_1)[/tex]
[tex]y - 1 = \dfrac{2}{3}(x - (-3))[/tex]
[tex]y - 1 = \dfrac{2}{3}(x + 3)[/tex]
[tex]y - 1 = \dfrac{2}{3}x + 2[/tex]
[tex]y = \dfrac{2}{3}x + 3[/tex]
Trey drives an average of 36 miles per day. How many days will it take him to drive 3,240 miles?
Answer:
90 days
Step-by-step explanation:
That = 3240 / 36
= 90 days
Answer:
90 days
Step-by-step explanation:
Hello, I think I can help you with this
You can easily solve this by using a simple rule of three.
Step one
Define
if the drives an average 36 miles per day,the how many days(x) will it take to drive 3240 miles :it is
1 day ⇔ 36 miles
x days ⇔ 3240 miles
the relation is
[tex]\frac{1\ day}{36\ miles}=\frac{x\ day}{3240\ miles}\\[/tex]
Step two
solve for x
[tex]\frac{1\ day}{36\ miles}=\frac{x\ day}{3240\ miles}\\\\x=\frac{1\ day*3240\ miles}{36\ miles}\\x=90\ days\\[/tex]
90 days
Have a great day.
What is the third quartile of this data set 20,21,24,25,28,29,35,37,42,43,44
Answer:
42
Step-by-step explanation:
The median is 29 . The third quartile is the middle number of the last 5 numbers.
This is 42
Answer:
42
Step-by-step explanation:
We are given that a data set
20,21,24,25,28,29,35,37,42,43,44
We have to find the value of third quartile of the given data set.
To find the third quartile we will use the given below formula
[tex]Q_3=\frac{3}{4}\times (n+1)^{th} term[/tex]
Where n=Total number of term
We have n=11
By using the formula
[tex]Q_3=\frac{3}{4}\times (11+1)^{th}[/tex] term
[tex]Q_3=9^{th}[/tex] term
[tex]9^{th}[/tex] term=42
Hence, third quartile=42
An aquarium has a length of n^ 2 +2 inches, a height of n + 5 inches, and a width of 10 inches. What is the volume, in cubic inches, of the aquarium, in terms of n ?
The formula of a volume of a rectangle prism:
[tex]V=lwh[/tex]
l - length
w - width
h - height
We have
[tex]l=n^2+2;\ w = 10,\ h=n+5[/tex]
Substitute:
[tex]V=(n^2+2)(10)(n+5)=(10n^2+20)(n+5)\\\\=(10n^2)(n)+(10n^2)(5)+(20)(n)+(20)(5)\\\\=10n^3+50n^2+20n+100[/tex]
Answer: V = (10n³ + 50n² + 20n + 100) in³The volume of the aquarium in terms of n is calculated by multiplying its length (n2 +2 inches), width (10 inches), and height (n + 5 inches) giving the formula V = (n2 + 2) imes (n + 5) imes 10, which expands to V = 10n3 + 60n2 + 20n + 100 cubic inches.
We use the formula V = length times width times height, where the volume V is the space inside the aquarium. The question provides the dimensions of the aquarium in terms of n: the length (n2 +2 inches), height (n + 5 inches), and width (10 inches).
To calculate the volume, simply multiply the dimensions together:
Length: n2 + 2 inchesHeight: n + 5 inchesWidth: 10 inchesVolume, V = (n2 + 2) imes (n + 5) imes 10
Expanding the expression gives us the volume V in cubic inches as a function of n:
V = 10n3 + 60n2 + 20n + 100 cubic inches
the volume of this rectangular prism is 5x^3. what does the coefficient 5 mean in terms of the problem?
Answer:
the length is 5 times the width of the prism
Step-by-step explanation:
the volume of this rectangular prism is [tex]5x^3[/tex]
volume of the prism = length * width * height
Length of the prism = 5x
Width = x
height =x
Length of the prism = 5x = 5* width of the prism
So, the length is 5 times the width of the prism
PLZ HELP!! The question is attached!
Answer:
Step-by-step explanation:
Subtract the 680 from 960, then divide the product by 52000 to get the answer
A Plummer is fixing a pipe with an interior diameter of 0.63 inches. He buys a replacement pipe that must fit inside the old pipe. He uses plumbing tape that will fill 0.15 inches off the space between the two pieces of pipe. The new pipe must be 0.1 inches smaller than the old pipe and tape so that it can fit inside. What is the largest interior diameter pipe he can buy that will still fit inside the old pipe?
The largest interior diameter of the new pipe that would still fit inside the old one is 0.38 inches, after taking into account the thickness of the plumbing tape and additional space requirement.
Explanation:The plumber is attempting to fit a new pipe into an old pipe with an interior diameter of 0.63 inches. We need to take into account the thickness of the plumbing tape that will add an extra 0.15 inches to the diameter, as well as the requirement that the new pipe must be 0.1 inches smaller to fit inside the old pipe.
To calculate the largest interior diameter the new pipe can have, we should do the following:
First, start with the old pipe's diameter, which is 0.63 inches. Deduct the thickness of the plumbing tape. This gives us 0.63 - 0.15 = 0.48 inches. Then, subtract the additional 0.1 inch requirement to provide space for the new pipe to fit. This gives us 0.48 - 0.1 = 0.38 inches.
So, the largest interior diameter of the new pipe that will fit in the old one is 0.38 inches.
Learn more about Pipe Diameter Calculation here:https://brainly.com/question/22714657
#SPJ12
Write an equation in slope-intercept form for the line that has a slope of -4 and passes through (1, 2).
A. y = -2x + 4
B. y = -4x + 2
C. y = -4x + 6
D. y = -4x + 9
y-y1 = m(x-x1) ..... point slope form
y-2 = -4(x-1) ... plug in the given info; solve for y
y-2 = -4x+4
y = -4x+4+2
y = -4x+6
Answer is choice C
Answer:
C. y = -4x + 6
Step-by-step explanation:
First write it in point-slope form ( because that is what you are given):-
y - y1 = m(x - x1):-
y - 2 = -4(x - 1)
y - 2 = -4x + 4
y = -4x + 6 (answer)
A real estate aqent earns a commission on a house she sells. Her first commission is 5% on the first 500,000 of the sale price of the house. She then earns a 6% comission for the amount sbove 500,000 of the sale price of the house. How much commission did the agent earn if she sold the house for 585,000?
Find the equation of the line parallel to the graph of 14x-7y=1 that passes through the point at (-2,4)
The equation of the line parallel to the graph of 14x - 7y = 1 that passes through the point at (-2, 4) is y = 2x + 8. The correct option is C.
To find the equation of the line parallel to the graph of 14x - 7y = 1 that passes through the point at (-2, 4), we first need to determine the slope of the given line. We can write the given equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
Starting with 14x - 7y = 1, we solve for y:
14x - 7y = 1-7y = -14x + 1y = 2x - 1/7The slope of the original line is 2, so a line parallel to it will also have a slope of 2. Using the point-slope form of a line equation, y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex]), and the point (-2, 4), we get:
y - 4 = 2(x + 2)y - 4 = 2x + 4y = 2x + 8Therefore, the equation of the line parallel to 14x - 7y = 1 and passing through (-2, 4) is y = 2x + 8.
Complete Question:
Find the equation of the line parallel to the graph of 14x-7y=1 that passes through the point at (-2,4).
Select the correct response:
[tex]\begin{aligned}A) \:& y=2 x+3 \\B)\: & y=\frac{1}{2} x+3 \\C) \:& y=2 x+8 \\D) \:& y=-\frac{1}{2} x-3\end{aligned}[/tex]
A pitcher of fruit punch holds 2 gallons. If 9 people share the entire pitcher equally, how much punch will each person get?
Answer:
2/9
Step-by-step explanation:
2÷9=2/9Use the function below to answer the question.
[tex]f(x)=x^3+7x^2+16x+12=(x+2)(x+2)(x+3)[/tex]
What is the multiplicity of the root -3 ?
Answer:
1
Step-by-step explanation:
(x +3) appears only once as a factor, hence the multiplicity of the root x=-3 is 1.
For every 2 bricks, 5 paving stones were used to build a backyard patio. James used a total of 120 bricks to complete his patio. Of the paving stones be used, 46% were tan in color while the rest were gray. How many gray paving stones were used to build the patio?
162
Step-by-step explanation:... (total paving stones) / bricks = 5 / 2
Multiplying by bricks gives ...
... (total paving stones) = (5/2)·bricks = 5/2·120 = 300
Then the number of gray paving stones is ...
... (gray stones) = (total paving stones) - (tan stones) . . . . tan + gray = total
... = (total paving stones) - 46% · (total paving stones) . . . . tan is 46% of total
... = (100% - 46%)·(total paving stones) = 54% · (total paving stones)
... = 54/100 · 300 . . . . put in the total number of paving stones
... (gray stones) = 162
Answer: 162
Step-by-step explanation:
helppppppppppppppppppppppppp
Answer:
It should be A, $12.75
Step-by-step explanation: Add 10.5+10.5+10.5+4.5+4.5+6.75= $47.25, subtract 60-47.25= $12.75
Write the equation of a line that passes through the points (0, -2) and (4, -5). Answer MUST be in standard form: Ax + By = C.
The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept → (0, b).
We have the points (4, -5) and (0, -2) → y-intercept → b = -2.
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Substitute:
[tex]m=\dfrac{-2-(-5)}{0-4}=\dfrac{-2+5}{-4}=\dfrac{3}{-4}=-\dfrac{3}{4}[/tex]
Therefore we have the equation of a line
[tex]y=-\dfrac{3}{4}x-2[/tex]
Convert to the standard form: [tex]Ax+By=C[/tex]
[tex]y=-\dfrac{3}{4}x-2\qquad\text{multiply both sides by 4}\\\\4y=-3x-8\qquad\text{add 3x to both sides}\\\\\boxed{3x+4y=-8}[/tex]
So for this, I will be putting the equation into slope-intercept form then rearranging it into standard form. Firstly, we need to solve for the slope. To do this, take the 2 coordinates given to us and solve as such:
[tex]\frac{-5-(-2)}{4-0}=-\frac{3}{4}[/tex]
Now, one of the coordinates given to us is (0,-2), which is the y-intercept. With all this info, our slope-intercept equation is [tex]y=-\frac{3}{4}x-2[/tex] . From here we can solve for the standard form.
Firstly, add 3/4x onto both sides of the equation:
[tex]\frac{3}{4}x+y=-2[/tex]
Now, it may appear that we are finished. However, 3/4 is not an integer (Integers are whole numbers). To make it an integer, we need to multiply both sides by 4:
[tex]3x+4y=-8[/tex]
Answer:In short, the standard form of this equation is 3x + 4y = -8.
A student has 20 pencils at the beginning of the school year. After a week, the student has 18 pencils left. If the student continues to use pencils at the same rate, which equation will represent pencils left after w weeks?
Answer: p = -2w + 20
Step-by-step explanation:
If the student had 20 pencils but now has 18 pencils, he uses pencils at a rate of 2 per week. So, m = -2 (negative because he is decreasing the amount of pencils). The student started with 20 pencils so b = 20
Use the y = mx + b but replace "y" with "p" and replace "x" with "w" and input the m and b as stated above:
p = -2w + 20
A health food store makes trail mix using dried fruit and nuts. The cost of the dried fruit is $2.50 per pound and the cost of the nuts is $2.00 per pound the total cost to make the trail mix is $225. If the total cost can be represented by the equation 2.5x+2y=225 what does the term 2.5x represent?
In the equation 2.5x + 2y = 225, the term 2.5x represents the cost of dried fruit, with 2.5 being the cost per pound.
In the provided equation 2.5x + 2y = 225, where x stands for the pounds of dried fruit and y represents the pounds of nuts, the term 2.5x signifies the cost associated with the dried fruit in making the trail mix.
The coefficient 2.5 represents the cost per pound of dried fruit, which is $2.50. Therefore, multiplying the pounds of dried fruit (x) by the cost per pound (2.5) gives the total cost of the dried fruit in the trail mix. In essence, 2.5x calculates the financial contribution of the dried fruit to the overall cost of producing the trail mix.
For example, if there are 10 pounds of dried fruit (x = 10), then 2.5 times 10 equals 25, representing the cost, in dollars, of the dried fruit in the trail mix. This interpretation extends to any quantity of dried fruit used in the trail mix.
In summary, the term 2.5x in the equation 2.5x + 2y = 225 specifically denotes the cost associated with the pounds of dried fruit (x) used in producing the trail mix.
For more such information on: equation
https://brainly.com/question/29174899
#SPJ6
At a basketball game, a vender sold a combined total of 223 sodas and hot dogs. The number of hot dogs sold was 57 less than the number of sodas sold. Find the number of sodas sold and the number of hot dogs sold.
Answer: 140 Hot dogs and 83 sodas.
Step-by-step explanation:
Alright, so we will say that h = hot dogs and s = sodas.
h + s = 223
I have used the guess and test strategy to get:
h = 140
140 - 57 = 83
s = 83
Check: 83 + 140 = 223
The total cost to rent a row boat is $16 times the number of hours the boat is used. How long can you rent the boat for $240
Answer: 15
from what i believe
Step-by-step explanation: i did the math that i thought it was and i did 240 divided by 16 and i got 15 hope this helps.
John is creating a Thanksgiving display at the store where he works, using only canned pumpkin and canned green beans. He needs to maintain a ratio of pumpkin to green beans of 5 to 1. If he wants to use a total of 114 cans, how many cans of green beans should he use?
Answer:
19
Step-by-step explanation:
The ratio of green beans (g) to pumpkin (p) is ...
... g : p = 1 : 5
Then the ratio of green beans to the total is ...
... g : (g+p) = 1 : (1+5) = 1 : 6
Since you have
... g/total = (1/6)
... g = total · 1/6
you can substitute 114 for the total to find ...
... g = 114 · 1/6 = 19
There is a line whose slope is 0 and whose y -intercept is 9. What is its equation in slope-intercept form?
Answer:
y = 0x + 9
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
here m = 0 and c = 9, hence
y = 0x + 9
The equation of a horizontal line is normally written as y = 9
with the x- term omitted
The equation of a line with a slope of 0 and a y-intercept of 9 is y = 9, which represents a horizontal line on the graph.
The student is asking about the equation of a line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Given that the slope (m) is 0, and the y-intercept (b) is 9, the equation of the line is simply y = 0x + 9. Since any number multiplied by zero is zero, this simplifies to y = 9.
Therefore, the equation of the line with a slope of 0 and a y-intercept of 9 in slope-intercept form is y = 9. This represents a horizontal line that crosses the y-axis at 9.
Tey is making a square frame for her painting. She is using 4 pieces of wood that are each 2.75 feet long. How much wood will tenly use to make the frame?
Answer:
11 feet wood will tenly use to make the frame.
Step-by-step explanation:
As given
Tey is making a square frame for her painting.
She is using 4 pieces of wood that are each 2.75 feet long.
Tenly uses wood to make the frame = Number of pieces of wood × Length of each pieces
Here
Number of pieces of wood = 4
Length of each pieces = 2.75 feet
Put in the above
Tenly uses wood to make the frame = 4 × 2.75
= 11 feet
Therefore 11 feet wood will tenly use to make the frame.
FInd the slope of a line
Answer:
The answer is: undefined or infinite
Hope this helps.
We can use the points (-1, 3) and (-1, 1) to solve.
Slope formula: y2-y1/x2-x1
= 1-3/-1-(-1)
= -2/0
= 0
This line is straight so it's undefined.
Hope This Helped! Good Luck!
Jose is going to order wrenches for his hardware store. He can order four different types and the table shows the profit margin for each type in tens of dollars and the probability. Which wrench should he order?
Answer:
B
Step-by-step explanation:
The expected value of profit margin is the sum of the product of profit margin and probability.
Wrench A:
... 10×.05 +20×.6 +30×.2 +40×.15 = 0.5 +12 +6 +6 = 24.5
Wrench B:
... (20+40)×.3 +(30+50)×.2 = 18 +16 = 34
Wrench C:
... 15×.4 +30×.5 +(45+60)×.05 = 6 +15 +5.25 = 26.25
Wrench D:
... 5×.2 +10×.4 +15×.15 +20×.25 = 1 +4 +2.25 +5 = 12.25
___
Clearly, Wrench B has the greatest expected profit margin. That would be the one Jose should order if he's trying to maximize his profit.
A number has the digits 1, 9 and 5 to the nearest 100 the number rounds to 600. What is the number?
Answer:
591
Step-by-step explanation:
the closest number to 600 out of every combo
195
159
951
915
519
591
Answer: 591
Step-by-step explanation:
From the digit 1, 9 and 5. The following numbers can be gotten if we use the 3 numbers.
159
195
519
591
915
951
Of all the numbers, the closest to 600 are 519 and 591.
To the nearest 100, 519 gives 500 while 591 gives 600. Therefore, the answer is 591.
Can someone please tell me if my answer is correct for this one.i need to know if the floor is positive, negative, zero or undefined. I say it's undefined
If you mean the y coordinate of that line, then it would be negative because it goes through -4 on the y axis.
On a factory floor 20 out of every 170 toy robots is defective what percent of toy robots are disaffected round the number to the nearest hundred
Answer:
We are given that there are total 170 toy robots
Number of defective robots out of total 170 toy robots [tex]=20[/tex]
We have to find the percentage of toy robots that are disaffected.
The percentage of toy robots that are disaffected is given below:
[tex]\frac{20}{170} \times 100[/tex]
[tex]0.1176 \times 100[/tex]
[tex]11.76[/tex]
Therefore, the percent of toy robots that are disaffected is [tex]\bold{11.76\%}[/tex]
Identify all the hyperbolas which open horizontally
Answer:
The hyperbolas which open horizontally are:
(x+2)^2/3^2-(2y-10)^2/8^2=1
(x-1)^2/6^2-(2y+6)^2/5^2=1
Step-by-step explanation:
A hyperbola with equation of the form:
(x-h)^2/a^2-(y-k)^2/b^2)=1 opens horizontally
Then, the hyperbolas which open horizontally are:
(x+2)^2/3^2-(2y-10)^2/8^2=1
(x-1)^2/6^2-(2y+6)^2/5^2=1
Answer:
[tex]\frac{(x-2)^2}{3^2}-\frac{(2y-10)^2}{8^2}=1[/tex]
and
[tex]\frac{(x-1)^2}{6^2}-\frac{(2y+6)^2}{5^2}=1[/tex]
Step-by-step explanation:
There are 2 types of hyperbolas:
Horizontal:
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]
Vertical:
[tex]\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1[/tex]
If the x term is positive then parabola is horizontal.
If the y term is positive then parabola is vertical.
so, only first two equations are in which x term is positive.
hence, equations are
[tex]\frac{(x-2)^2}{3^2}-\frac{(2y-10)^2}{8^2}=1[/tex]
and
[tex]\frac{(x-1)^2}{6^2}-\frac{(2y+6)^2}{5^2}=1[/tex]
Which of the following is equal to cos 35
A) sin 35
B)cos 55
C) sin 55
D) cos 145
Explain why it is equal
Answer:
B) cos 55
Step-by-step explanation:
Consider a right angle triangle with 35 angle, the other angle = 180 - 90 - 35 = 55
sin 35 = opposite side of 35 angle / hypothesis
Opposite side of 35 angle is the same as the adjacent side of 55 angle
sin 35 = adjacent side of 65 angle / hypothesis = cos 55
The answer is B.
Please please help me out!
Answer: $1.25 decrease
Step-by-step explanation:
I am not positive but I think this is how you calculate it:
(.25)($10) + (.75)(-$5)
= $2.50 + -$3.75
= -$1.25