An equation is formed of two equal expressions. The equation 7*e^0.1t=47 can be expressed as t=[ln (47/7)]/0.1.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The equation 7*e^0.1t=47 in terms of logarithm in terms of base-e can be solved as,
[tex]7e^{0.1t}=47\\\\e^{0.1t}=\dfrac{47}{7}\\\\0.1 t = {\rm ln}(\dfrac{47}{7})\\\\t = \dfrac{ {\rm ln}(\frac{47}{7})}{0.1}[/tex]
Hence, the equation 7*e^0.1t=47 can be expressed as t=[ln (47/7)]/0.1.
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A car travels 294 miles per hour on a full tank of gas . the cars gas tank holds 14 gallons. how many yards per gallon can this car travel?
Answer:
36960 yards
Step-by-step explanation:
294/14=21
1 gallon is 21 miles
1 mile is 1760 yard
21 miles is 36960 yards
36960 yard is the answer assuming 14 gallons is a full tank of gas
A helicopter travels 30 kilometers in 3 minute. What is the speed in terms of
33
10
kilometers per minute?
The speed is the distance covered by an object at a particular time. The speed of the helicopter is equal to 10 kilometer/minute.
What is speed?The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.
[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]
Given the helicopter travels 30 kilometers in 3 minute. Therefore, the speed of the helicopter is equal to,
Speed = 30 kilometer/ 3minutes = 10 kilometer/minute.
Hence, the speed of the helicopter is equal to 10 kilometer/minute.
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Which of the following statements are true?
Choose all answers that apply:
B
The equation represents a proportional relationship.
The unit rate of change of y with respect to a is
The slope of the line is 2.5.
A change of 5 units in a results in a change of 2 units in y.
A change of 2 units in a results in a change of 5 units in y.
2|5
Based on the function given of y = 2.5x, the true statements are:
The equation represents a proportional relationship.The slope of the line is 2.5.A change of 2 units in x results in a change of 5 units in y.What does the function represent?The equation y = 2.5x is a proportional relationship because y increases by a certain amount when x increases. That amount is shown by the slope of the line which is 2.5.
For instance, if there is a change of 2 in x, the change in y would be:
= 2.5 × x
= 2.5 x 2
= 5
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HELP I can’t figure it out
Answer:
[tex]\huge\bold\color{pink}{- Magdonal -}[/tex]
[tex]\blue{\rule{50pt}{999999pt}} \purple{\rule{50pt}{999999pt}} \
\green{\rule{27pt}{999999pt}} \blue{\rule{10pt}{999999pt}} \
[/tex]
Solve the system of equations using substitution.
y=x+2,5x-4y=-3
Answer:
x=5 and y=7
Step-by-step explanation:
Just substitute in y=x+2 into the equation 5x-4y=-3 to get 5x-4(x+2)=-3 which simplifies to x=5. Substitute x into y=x+2 to find y=7
A triangular prism. The rectangular sides are 3 feet by 2 feet, 3 feet by 2.5 feet, and 3 feet by 1.5 feet. The 2 triangular sides have a base of 2 feet and height of 1.5 feet.
Trenton is building a skateboarding ramp in the shape of a triangular prism. According to his plan, the ramp would have a base of 2 feet, a height of 1.5 feet, and a length of 3 feet. The riding surface would measure 2.5 feet.
If Trenton wants to cover all faces of the ramp with plywood, how much plywood will he need to buy?
Trenton will need
square feet of plywood.
The amount of plywood needed by Trenton = total surface area of the triangular prism-shaped ramp = 21 ft².
What is the Surface Area of a Triangular Prism?Total surface area of a triangular prism = (perimeter of triangular base × length of prism) + 2(area of triangular base) = (s1 + s2 + s3 × L) + 2(1/2 × b ×h).
The amount of plywood needed to cover the ramp = total surface area of the triangular prism-shaped ramp.
We are given the parameters:
s1 = 2 fts2 = 1.5 fts3 = 2.5L = 3 ftb = 2 fth = 1.5 ftTotal surface area of the triangular prism-shaped ramp = (s1 + s2 + s3)L + 2(1/2 × b ×h) = (2 + 1.5 + 2.5)3 + 2(1/2 × 2 ×1.5)
= (18) + (3)
Total surface area = 21 ft²
Trenton will need 21 square feet of plywood.
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Find the value of each variable.
Step-by-step explanation:
b is per the identity of angles on parallel lines when intersected by one inclined line the same as the 40° angle.
so,
b = 40°
due to the parallel nature of the 2 lines there is a symmetry effect for such shapes inscribed a circle. the upper and the lower triangle must be similar. and when applying a vertical line through the central crossing point, everything to the left is mirrored by everything on the right.
so, angle c must be equal to angle b.
c = 40°
and as the sum of all angles in a triangle is always 180°, d is then
d = 180 - 40 - 40 = 100°
the interior angle of the arc angle a is the supplementary angle of d (together they are 180°), because together with d they cover the full down side of the top-left to bottom-right line.
interior angle to a = 180 - 100 = 80°
due to the symmetry again, the arc angle opposite to a is the same as a.
as we know, the interior angle to a pair of opposing arc angles is the mean value of the 2 angles.
so, we have
(a + a)/2 = 80
2a/2 = 80
a = 80°
there might (and actually should) be some more direct approaches for "a" out of the other pieces of information, but that was the most straight one right out of my mind, and I don't spend time on finding additional shortcuts, when I have already a working approach.
What is the midpoint of the segment shown below?
Answer:
answer is c (0,2)
hope it helps
Simplify the expression 3x(x – 12x) + 3x2 – 2(x – 2)2. Which statements are true about the process and simplified product? Select three options
To solve the problem we must know about the Like terms and expressions.
What is an Expression?In mathematics, an expression is a set of numbers, variables, and mathematical operations formed according to rules.
Given ;
[tex]3x(x - 12x) + 3x^2 - 2(x - 2)^2[/tex]
To solve the algebraic expression,
[tex]3x(x - 12x) + 3x^2 - 2(x - 2)^2\\\\3x(x - 12x) + 3x^2 - 2(x^2 - 4x + 4)\\\\3x(x - 12x) + 3x^2 - 2x^2 + 8x - 8\\\\3x^2 - 36x^2 + 3x^2 - 2x^2 + 8x - 8\\\\-33x^2 + x^2 + 8x - 8\\\\\\-32x^2 + 8x - 8\\[/tex]
To solve the problem we must know about the Like terms and expressions.
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Rachael took her dogs, Rico, Mocha, and Biscuit, to the vet. Rico weighed 45.7 kilograms, Mocha weighed 15.5 kilograms, and Biscuit weighed 22.1 kilograms. How much more did Rico weigh than Biscuit?
Subtraction is a mathematical operation that reflects the removal of things from a collection. The amount by which Rico weighs more than Biscuit is 23.6 kilograms.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
Given Rico weighed 45.7 kilograms, Mocha weighed 15.5 kilograms, and Biscuit weighed 22.1 kilograms. Therefore, the amount by which Rico weighs more than Biscuit is,
Difference = 45.7 kgs - 22.1 kgs = 23.6 kgs
Hence, the amount by which Rico weighs more than Biscuit is 23.6 kilograms.
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Question content area top
Part 1
Darcy gave her nail technician a $5.10 tip. The tip was 15% of the cost of the manicure. Write an equation to find b, the cost of the manicure
Answer:
Let b the cost of the manicure
15% of b= 5.10$
15% × b= 5.10$
b= 5.10×100/15
b= 34$
Explain how to solve 5^(x-2)=8 using log base b of y equals log y over log b. include the solution for x in your answer. round your answer to the nearest thousandth.
The value of x will be equal to 2.477.
What is a logarithm?The logarithm is the inverse function of exponentiation in mathematics. That is, the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised in order to obtain that number x.
The given expression will be solved as follows;-
[tex]5^{x-2}= 8[/tex]
Taking Log on both sides.
[tex]Log_e 5^{x-2}=Log_e8[/tex]
(x-2) Log5 = Log 8
( x-2) = Log8 / Log 5
(x - 2) = Log 8 - Log 5
(x - 2 ) = Log 3
x-2 = 0.477
x = 2.477
Therefore the value of x will be equal to 2.477.
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The board of directors of streamlined airlines has declared a dividend of $4,300,000. the company has 400,000 shares of preferred stock that pay $0.70 per share and 2,750,000 shares of common stock. after finding the amount of dividends due the preferred shareholders, calculate the dividend per share of common stock. (round your answer to the nearest cent if necessary)
The dividend per share of common stock is $1.46.
What is the dividend per share of common stock?The first step is to determine the total value of the dividends that was paid to the preferred stock holders.
Total value = 400,000 x $0.70 = $280,000
The total value of the common stock dividends = $4,300,000 - $280,000 = $4,020,000
Dividend per share = 4,020,000 / 2,750,000 = $1.46
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What is the solution to x² - 11x + 24 = 0
Answer:
(x - 8)(x - 3)=0
x - 8=0 or x - 3=0
x =8 x =3
6. In both Mr. Jacquez's Math 2 classes, Period 2 and Period 3 were given the same test. The table below shows the results from the two classes.
a. Find the probability that a randomly selected student from Period 2's class failed the test.
b. Find the probability that a randomly selected student who failed the test is from Period 3's class.
*would help out big time if someone could help me out, thankyou*
Answer: pass 12 fail 12 passes 15 fail1 3
Step-by-step explanation:
pass 12 fail 12
pass 15 fail 13
Twenty-five students are competing in a Science Fair. In how many ways can 3 students win first, second, and third place?
A) 2.6 · 10^24 B) 3.9 · 10^25 C) 13,800 D) 19,656
Please help
Answer:
C
Step-by-step explanation:
[tex]\frac{25!}{(25-3)!} =13800[/tex]
A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function h = −16t2 + 36t + 10. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. What is the ball’s maximum height?
The ball's maximum height is 30.25 feet.
What is quadratic equation?A quadratic equation in math is a second-degree equation of the form ax² + bx + c = 0. Here a, b, are the coefficients, c is the constant term, and x is the variable.
Given:
h= -16t²+36t+10
Differentiate w.r.t. 't',
h' = -32t+36
When h=0, that will be the maximum height
32t= 36
t= 9/8
t= 1.125 sec.
So, The maximum height is
h(1.123)= -16(1.125)² + 36*1.125+10
h(1.125) = 30.25 feet.
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To counteract race-related violence, the fourteenth amendment was ratified to give african american men the right to vote. grant citizenship to african americans. establish military control of the south. make white supremacy groups illegal.
To counteract race-related violence, the 14 th amendment was ratified to grant citizenship to African Americans. Thus, option B is correct.
What is the fourteenth amendment?The main purpose of the 14th Amendment is to guarantee and protect the citizenship and rights of African Americans.
The 14th Amendment was ratified in 1868, and it granted citizenship to all the people that born or naturalized in the United States.
This was a particularly significant development for former slaves.
This is to give them equal protection from the laws.
To counteract race-related violence, the 14 th amendment was ratified to grant citizenship to African Americans. Thus, option B is correct.
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Solve for x. Round to nearest tenth
SOMEONE PLEASE HELP ME WITH THIS ILL GIVE YOU BRAINLIST ANSWER
Image above
Done!
the equation y=6.75x models the cost in dollars to purchase x pounds of steak at grocery store 1.
The true statement is the cost of steak at grocery store 1 is $0.75 less per pound than at grocery store 2.
What is the true statement?In store 1, the cost of 1 pound of steak is $6.75.
Cost of 1 pound of steak in store 2 is 15 /2 = $7.50
Difference in the cost : $7.50 - $6.75 = $0.75
Here is the complete question:
The equation y = 6.75x models the cost, in dollars, to purchase x pounds of steak at grocery store 1. This table shows the cost to buy different weights of steak at grocery store 2.
Cost of Steak at Grocery Store 2
Weight (pounds) Cost
2..........................$15.00
3..........................$22.50
5......................... $37.50
9......................... $67.50
Which statement is true?
answer choices
The cost of steak at grocery store 1 is $0.75 less per pound than at grocery store 2.
The cost of steak at grocery store 1 is $0.75 more per pound than at grocery store 2.
The cost of steak at grocery store 1 is $0.50 less per pound than at grocery store 2.
The cost of steak at grocery store 1 is $0.50 more per pound than at grocery store 2. R
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Twice a number x increased by 32 is translated to 2x+32
Answer:
If you are asking if that's correct then yes it is
Step-by-step explanation:
r,s and t are the vectors given by 4i+j,3i+2j and 4i +j respectively.find [r+s+t]
Answer:
11i+4j
Step-by-step explanation:
add the i's together and the j's together.
Use Pemdas to evaluate: 5c - 19, c=10
Can you solve this??
[tex]9-\underline{9\div 9} + 9 - \underline{9 \div 9}\implies 9-\underline{1}+9-\underline{1}\implies 8+9-1\implies 17-1\implies 16\\[/tex]
recall PEMDAS, MD are before AS, and both are performed from left to right.
Answer:
20
Step-by-step explanation:
first lets apply PEMDAS
[tex]9 - (9 \div 9) + 9 - (9 \div 9) [/tex]
9 ÷ 9 = 1
1 × (-) = -1
9-(-1)= 10
( than do the same for other side )
and than you get
[tex]10 + 10[/tex]
the answer is 20
8 Lizzie started a new business that had a profit of $31,124 at the end of the first year. Her
financial advisor estimates her profit will increase by 6% a year. Assuming her advisor is
correct, determine her total profit, to the nearest cent, for the first ten years.
Using an exponential function, it is found that her total profit for the first ten years is of $422,426.72.
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem, we have that the initial value and the growth rate are given as follows:
A(0) = 31124, r = 0.06.
Hence the profit function is given by:
[tex]P(t) = 31124(1.06)^t[/tex]
Then, the total profit over the first 10 years is given by:
[tex]\int_{0}^{10} P(t) dt[/tex]
[tex]\int_{0}^{10} 31124(1.06)^t dt[/tex]
[tex]\frac{31124}{\ln{1.06}} \times (1.06)^t|_{t = 0}^{t = 10} = 422,426.72[/tex]
Thus, her total profit for the first ten years is of $422,426.72.
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Given y=3x-3, find y if x=4
Answer: Given y=3x-3, find y if x=4
y=3x-3
x=4
y=3(4)-3
y=12-3
y=9
Step-by-step explanation: hopes this helps
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si se utilizan 9.01 litros de pintura para pintar 1.7 metros cuadrados de pared,cuantos litros de pntura necesitanpara pinatr 1 metro cuadrado de pared
Usando proporciones, hay que se necessita 8.42 litros de pintura para pintar 1 metro cuadrado de pared.
¿Qué es una proporción?Una proporción es una fracción de la cantidad total, e puede ser encontrada aplicando una regla de três.
En este problema, se utilizan 9.01 litros de pintura para pintar 1.7 metros cuadrados, por eso, la cantidad relativa a 1 metro cuadrado es dada por:
c = 9.01/1.7 = 8.42 litros.
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PLEASE HELP ANSWER ALL!!! WITH DIAGRAM!!!
You toss a coin (heads or tails), then spin a three-color spinner (red, yellow, or blue). Complete the tree diagram, and then use it to find a probability.
1. Label each column of rectangles with "Coin toss" or "Spinner."
2. Write the outcomes inside the rectangles. Use H for heads, T for tails, R for red, Y for yellow, and B for blue.
3. Write the sample space to the right of the tree diagram. For example, write "TY" next to the branch that represents "Toss a tails, spin yellow."
4. How many outcomes are in the event "Toss a tails, spin yellow"?
5. What is the probability of tossing tails and spinning yellow?
Answer:
For Questions 1 , 2 and 3 check the attached diagram
4. How many outcomes are in the event "Toss a tails, spin yellow"?
There is only one outcome ‘TY’ in this event .
5. What is the probability of tossing tails and spinning yellow?
[tex]p\left( TY\right) =\frac{1}{6}[/tex]
Step-by-step explanation:
Diagram
frank says that he typically makes about $27 per day because the mode is 27. is frank's conclusion appropriate? explain.
If Frank says that he typically makes about $27 per day because the mode is 27. Yes, Frank's conclusion is appropriate. And mean is 28.
The complete question is given below.
Frank kept track of the amount of money he earned each day for 2 weeks. The amounts, in dollars, are listed below. 25, 30, 24, 20, 20, 22.5, 75, 27, 27, 22, 22, 27, 22.5, 28 Part A Find and calculate the measures of center and variability that best summarize Frank's data. Explain. Part B Frank says that he typically makes about $27 per day because the mode is 27. Is Frank's conclusion appropriate? Explain.
What are statistics?Statistics is the study of collection, analysis, interpretation, and presentation of data or to discipline to collect, and summarise the data.
The data is given below.
25, 30, 24, 20, 20, 22.5, 75, 27, 27, 22, 22, 27, 22.5, 28.
The measures of center and variability that best summarize Frank's data will be
Mean = (25+30+24+20+20+22.5+75+27+27+22+22+27+22.5+28) / 14
Mean = 392 / 14
Mean = 28
If Frank says that he typically makes about $27 per day because the mode is 27.
Yes, Frank's conclusion is appropriate.
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Which polynomial function has a leading coefficient of 1 and roots (7 i) and (5 – i) with multiplicity 1? f(x) = (x 7)(x – i)(x 5)(x i) f(x) = (x – 7)(x – i)(x – 5)(x i) f(x) = (x – (7 – i))(x – (5 i))(x – (7 i))(x – (5 – i)) f(x) = (x (7 – i))(x (5 i))(x (7 i))(x (5 – i))
It looks like you might have intended to say the roots are 7 + i and 5 - i, judging by the extra space between 7 and i.
The simplest polynomial with these characteristics would be
[tex]f(x) = (x - (7 + i)) (x - (5 - i))[/tex]
but seeing as each of the options appears to be a quartic polynomial, I suspect f(x) is also supposed to have only real coefficients. In that case, we need to pair up any complex root with its conjugate to "complete" f(x). We end up with
[tex]f(x) = (x - (7 + i)) (x - (7 - i)) (x - (5 - i)) (x - (5 + i))[/tex]
which appears to most closely resemble the third option. Upon expanding, we see f(x) does indeed have real coefficients:
[tex]f(x) = (x^2 - (7^2 - i^2)) (x^2 - (5^2 - i^2)) = (x^2 - 8) (x^2 - 6) = x^4 - 14x^2 + 48[/tex]
Answer:
C on edge 23
Step-by-step explanation:
because i said so