solve the inequality 4t^2 ≤ 9t-2 please show steps and interval notation. thank you!​

If we simplify, both Joe and Hope factored the polynomial correctly but Joe didn't complete it fully.

The first binomial can be further factored:

The quadratic expression needs to have two roots in order to be factored as two binomials.

The discriminant must be positive or zero:

We have a = 3, b = k, c = -8

So we get following inequality:

Since k² is positive for any value of k, the solution is any value of k:

Hope this attachment helps you.

Answer:

The first mechanic charged $ 85 an hour, and the second mechanic charged $ 55 an hour.

Step-by-step explanation:

Given that two mechanics worked on a car, and the first mechanic worked for 10 hours, and the second mechanic worked for 5 hours, and together they charged a total of $ 1125, to determine what was the rate charged per hour by each mechanic if the sum of the two rates was $ 140 per hour, the following calculation must be performed:

1125/15 = X

75 = X

80 x 10 + 60 x 5 = 800 + 300 = 1100

85 x 10 + 55 x 5 = 850 + 275 = 1125

Therefore, the first mechanic charged $ 85 an hour, and the second mechanic charged $ 55 an hour.

Answer:

24/145

Step-by-step explanation:

Trigonometric identities are equalities involving trigonometric functions and remains true for entire values of the variables involved in the equation.

Some trigonometric identities are:

sin(a + b) = sinacosb + cosasinb; sin(a - b) = sinacosb - cosasinb

cos(a + b) = cosacosb - sinasinb; cos(a - b) = cosacosb + sinasinb

Given that sin a = 3/5. sin a = opposite/hypotenuse.

Hence opposite = 3, hypotenuse = 5. using Pythagoras:

hypotenuse² = opposite² + adjacent²

5² = 3² + adjacent²

adjacent² = 16

adjacent = 4

Given that sin a = 3/5. a = sin⁻¹(3/5) = 36.86

cos a = cos 36.86 = 4/5

cos b = -20/29; b = cos⁻¹(-20/29) = 133.6

sinb = sin(133.6) = 21/29

sin(a + b) = sinacosb + cosasinb = (3/5 * -20/29) + (4/5 * 21/29) = -12/29 + 84/145

sin(a + b) = 24/145

Answer:

17

Step-by-step explanation:

because they are both above 5 so add 1

Answer:

80 ft

Step-by-step explanation:

The formula for finding the surface area of a rectangular prism is:

A = 2(wl + hl + hw)

A = 2({4x3} + {4x3} + {4x4})

A = 2 (12 + 12 + 16)

A= 2 ( 40)

A = 80 feet

Answer:

l = 1920 cm

Step-by-step explanation:

Given that,

The radius of circle, r = 8 cm

The central angle is 240 degrees

We need to find the length of the arc. We know that,

[tex]l=r\theta[/tex]

Where

l is the length of the arc

So,

[tex]l=8\times 240[/tex]

[tex]\implies l=1920\ cm[/tex]

so, the length of the arc is equal to 1920 cm.

Answer:

[tex]\displaystyle V = \frac{625 \pi}{2}[/tex]

General Formulas and Concepts:

Algebra I

Calculus

Integrals

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:                                                       [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Shell Method:                                                                                                         [tex]\displaystyle V = 2\pi \int\limits^b_a {xf(x)} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

y = x²

y = 0

x = 5

Step 2: Identify

Find other information from graph.

See Attachment.

Bounds of Integration: [0, 5]

Step 3: Find Volume

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Applications of Integration

Book: College Calculus 10e

Answer:

please mark me brainlist

Step-by-step explanation:

Answer:

(0, -9)

Step-by-step explanation:

The y intercept is the y value when x =0

(0, -9)

answer choice a

x^2 - 5x - 1 = 0

a=1, b=-5, and c=-1

next you plug in the numbers into the quadratic formula

-(-5) plus or minus the square root of (-5)^2 - 4(1)(-1)/ 2(1)

after you simply, you should get 5 plus or minus the square root of 29, which is answer choice a

Answer:

946 people

Step-by-step explanation:

Find how many you would predict to be satisfied by multiplying 1,100 by 0.86:

1,100(0.86)

= 946

So, you could expect 946 people to be satisfied

the SAS similarity theorem

Answer:

Translation

Step-by-step explanation:

A translation is when the triangle is moved around on the graph without it being reflected or changed in any way. I will be the same exact triangle, just with different coordinates.

Hope this helps!

Step-by-step explanation:

ΔABC, where AB = 8 cm, BC = 6 cm, B = 70° Construction: (i) Draw the ∆ABC with the given measurements. (ii) Construct the perpendicular bisector at any two sides (AB and BC) and let them meet at S which is the circumcircle. (iii) S as centre and SA = SB = SC as radius, draw the circumcircle to pass through A, B, and C. Circum radius = 4.3cm .draw-triangle-abc-where-cm-bc-and-70-and-locate-its-circumcentre-and-draw-the-circumcircle

Answer:

[tex]8^{3(n-1)+1}[/tex]

Step-by-step explanation:

Answer:

0.3711 = 37.11% probability that 5 or more of the 100 people will get the flu

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they will develop the flu after getting the shot, or they will not. The probability of a person developing the flu after getting the shot is independent of any other person, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The probability that a person will develop the flu after getting a flu shot is 0.04.

This means that [tex]p = 0.04[/tex]

Random sample of 100 people:

This means that [tex]n = 100[/tex]

What is the probability that 5 or more of the 100 people will get the flu?

This is:

[tex]P(X \geq 5) = 1 - P(X < 5)[/tex]

In which

[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]

So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{100,0}.(0.04)^{0}.(0.96)^{100} = 0.0169[/tex]

[tex]P(X = 1) = C_{100,1}.(0.04)^{1}.(0.96)^{99} = 0.0703[/tex]

[tex]P(X = 2) = C_{100,2}.(0.04)^{2}.(0.96)^{98} = 0.1450[/tex]

[tex]P(X = 3) = C_{100,3}.(0.04)^{3}.(0.96)^{97} = 0.1973[/tex]

[tex]P(X = 4) = C_{100,4}.(0.04)^{4}.(0.96)^{96} = 0.1994[/tex]

Then

[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0169 + 0.0703 + 0.1450 + 0.1973 + 0.1994 = 0.6289[/tex]

[tex]P(X \geq 5) = 1 - P(X < 5) = 1 - 0.6289 = 0.3711[/tex]

0.3711 = 37.11% probability that 5 or more of the 100 people will get the flu

Answer:

4:30

because 9:30 minus 4:30 = 5:00 and 5:00 minus 30 =4:30

Answer:240 square centimeters

Step-by-step explanation:

1. 10x7=70

2. 7x10=70

3. 25x4=100

70+70+100=240

Answer:

85 mi

Step-by-step explanation:

Let d = the distance in miles traveled

Let M = the time in hours for Maria to travel d miles

[tex]m+\frac{3}{4} =[/tex] time in hours for Ricky to travel d miles

(Note that [tex]\frac{3}{4}[/tex] hrs = 45 min)

----------------------

Maria's equation:

d = 51m

Ricky's equation:

d = 24 · [tex](m+\frac{3}{4} )[/tex]

----------------------

Substitution:

51m = 24 · [tex](m+\frac{3}{4} )[/tex]

51m = 24m + 45

6m = 10

m = [tex]\frac{5}{3}[/tex]

----------------------

d = 51m

d = 51 · [tex](\frac{5}{3})[/tex]

d = 85

----------------------

The distance traveled is 85 mi

If it takes Ricky, traveling at 24 mph, 45 minutes longer to go a certain distance than it takes Maria traveling at 51 mph, the distance traveled is 85 miles

Speed is the ratio of distance traveled to time taken. Mathematically:

Distance = Speed/Time

According to the given question:

Set up the Maria equation:

d = 51m

Set up Ricky's equation:

d = 24 · (m+3/4)

Substitute

51m = 24 · (m+3/4)

51m = 24m + 45

6m = 10

m = 5/3

Determine the required distance

d = 51m

d = 51 · 5/3

d = 85

Hence the distance traveled is 85 mile

Learn more on distance and speed here: https://brainly.com/question/26046491

Answer:

0.5 = 50% probability that a randomly chosen sample of glass will break at less than 509 MPa

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 509 MPa with a standard deviation of 17 MPa.

This means that [tex]\mu = 509, \sigma = 17[/tex]

What is the probability that a randomly chosen sample of glass will break at less than 509 MPa?

This is the p-value of Z when X = 509. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{509 - 509}{17}[/tex]

[tex]Z = 0[/tex]

[tex]Z = 0[/tex] has a p-value of 0.5

0.5 = 50% probability that a randomly chosen sample of glass will break at less than 509 MPa

Answer:

0.924

Step-by-step explanation:

R² = 0.854

R = √0.854

R = 0.924

Hence, the correlation Coefficient of electricity tarrif is 0.924 ; this correlation Coefficient value, depicts a strong positive correlation between machine hours and cost of electricity. And can he interpreted to mean that ; Electricity tarrif increases as machine hours increases and also decreases as machine hours decreases.

Answer:

Ideez

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

cos60° = x / 10

10cos60° = x

10cos60° = 5

9514 1404 393

Answer:

  Kim

Step-by-step explanation:

The ratio of Kim's distance to Adrian's distance is ...

  (9/10)/(3/5) = (9/10)/(6/10) = 9/6 = 3/2 = 1.5

__

You need to be very careful with the wording here. Kim ran 1 1/2 times as far as Adrian. That is, she ran Adrian's distance plus 1/2 Adrian's distance.

If we take the wording "1/2 times farther" to mean that 1/2 of Adrian's distance is added to Adrian's distance, then Kim is correct.

_____

In many Algebra problems, you will see the wording "k times farther" to mean the distance is multiplied by k. If that interpretation is used here, neither claim is correct, as Kim's distance is 1 1/2 times farther than Adrian's.

On the other hand, if the value of "k" is expressed as a percentage, the interpretation usually intended is that that percentage of the original distance is added to the original distance. Using this interpretation, Kim's distance is 50% farther than Adrian's. (Note the word "times" is missing here.)

__

Since Adrian ran 1 5/10 the distance Kim ran, Adrian's claim is incorrect regardless of the interpretation. If you require one of the two to be correct, then Kim is.

Answer:

1. (x,y) → (y,x)

Step-by-step explanation:

Coordinate of point E:

Before the transformation, the coordinate of point E was given by (3,-6).

After the transformation, we have E'(-6,3), which eliminates options 2 and 3.

For the other points, we will also get, (x,y) -> (y,x), which is the rule given when the original figure is reflected over the line y = x, and thus, the correct answer is given by option 1.

Answer:

The function that passes through (0, 0) is [tex]f(x) = \frac{1}{6}\cdot e^{2\cdot x^{3}} - \frac{1}{6}[/tex].

Step-by-step explanation:

Firstly, we integrate the function by algebraic substitution:

[tex]\int {x^{2}\cdot e^{2\cdot x^{3}}} \, dx[/tex] (1)

If [tex]u = 2\cdot x^{3}[/tex] and [tex]du = 6\cdot x^{2} dx[/tex], then:

[tex]\int {e^{2\cdot x^{3}}\cdot x^{2}} \, dx[/tex]

[tex]\frac{1}{6}\int {e^{u}} \, du[/tex]

[tex]f(u) = \frac{1}{6}\cdot e^{u} + C[/tex]

[tex]f(x) = \frac{1}{6}\cdot e^{2\cdot x^{3}} + C[/tex]

Where [tex]C[/tex] is the integration constant.

If [tex]x = 0[/tex] and [tex]f(0) = 0[/tex], then the integration constant is:

[tex]\frac{1}{6}\cdot e^{2\cdot 0^{3}} + C= 0[/tex]

[tex]C = -\frac{1}{6}[/tex]

Hence, the function that passes through (0, 0) is [tex]f(x) = \frac{1}{6}\cdot e^{2\cdot x^{3}} - \frac{1}{6}[/tex].

Answer:

20 million = 2 crore

Step-by-step explanation:

Here we will show you how to convert 20 million to crores (twenty million in crores). This may be useful if you for example want to convert 20 million rupees to crore rupees or 20 million dollars to crore dollars.

In some parts of the world like the United States, large numbers are separated with commas in three-digit-interval format like this:

...,BBB,MMM,TTT,HHH

BBB = billions

MMM = millions

TTT = thousands

HHH = hundreds

In certain parts of Asia, the format is a little different. From right to left, it starts out with three digits followed by a comma like the US, but after that, it is in intervals of two digits like this:

..,AA,CC,LL,TT,HHH

AA = arabs

CC = crores

LL = lakhs

TT = thousands

HHH = hundreds

Below we have displayed 20 million with the two number systems, based on the information above:

MM,TTT,HHH

20,000,000

=

C,LL,TT,HHH

2,00,00,000

When you match up 20 million with the C,LL,TT,HHH format above, you can see what 20 million is in crores. The answer to 20 million in crores is as follows:

20 million

= 2 crore