Justin has ridden 34 miles of a bike course. The course is 40 miles long. What percentage of the course has Justin ridden so far?

Answer:

Step-by-step explanation:

When it's clear, the easiest way to do the problem is to used the x and y  intercepts.

This question is one of the clear one.

The x intercept is 2,0

The y intercept is 0,1

You want the slope.

m = (y2 - y1)/(x2 - x1)

y2 = 1

y1 = 0

x2 = 0

x1 = 2

m = (1 - 0)/(0 - 2)

m = 1 / -2

m = -1/2

In this case the slope and gradient have the same value --   - 1/2 or - 0.5

Step-by-step explanation:

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The average yearly growth rate of the height of the tree is 2 1/3 feet

Given:

original height of the pine tree = 40 1/2 feet

Height in next 7 1/2 years = 57 feet

Change in height = Height in next 7 1/2 years - original height of the pine tree

= 57 height - 40 1/2 feet

= 17 1/2 feet

Average growth rate yearly = Change in height / number of years

= 17 1/2 feet ÷ 7 1/2 years

= 35/2 ÷ 15/2

= 35/2 × 2/15

= (35 × 2) / (2 × 15)

= 70/30

= 2 10/30

= 2 1/3 feet

Therefore, the average yearly growth rate of the height of the tree is 2 1/3 feet

Learn more about fraction:

https://brainly.com/question/1622425

Answer:

π/10

Step-by-step explanation:

α=-19π/10=-19π/10+2π=(-19π+20π)/10=π/10

first you have to pick any two points on the line

(-3,4) and (0,-2)

then you subtract the y values

-2-4= -6

after that you subtract the x values

0 - (-3)= 3

the slope is -6/3, or -2

Answer:

4/3 1.333 1 1/3

Step-by-step explanation:

Hope it helps.

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Answer:

88 ft

Step-by-step explanation:

Let's say the shortest piece has length 2x, so the medium piece has length 5x and the longest piece has length 8x. Added together, they equal 165, so

2x + 5x + 8x = 165

15x = 165

divide both sides by 15 to isolate x

x = 11

8x = longest piece = 88 ft

Answer:

15 lessons for $ 80

Step-by-step explanation:

In case 1

Cost of 1 lesson = $10

In case 2

Cost of 1 lesson = 40/5 = $8

In case 3

Cost of 1 lesson = 80/10 = $8

In case 4

Cost of 1 lesson = 80/15 = $ 5.33

Hence,

The best deal is case 4 i.e 15 lessons for $ 80

Answer:

x < -5

Step-by-step explanation:

3 ( -2x - 4 ) > 18

→ Expand the brackets

-6x - 12 > 18

→ Add 12 to both sides

-6x > 30

→ Divide both sides by -6

x < -5

Answer:

[tex]\boxed {\boxed {\sf x< -5}}[/tex]

Step-by-step explanation:

We are asked to solve the following inequality for x.

[tex]3(-2x-4) > 18[/tex]

Solve for x by isolating it and performing the inverse operations.

3 is being multiplied by (-2x-4). The inverse operation of multiplication is division. Divide both sides of the inequality by 3.

[tex]\frac {3(-2x-4)}{3} > \frac{18}{3}[/tex]

[tex](-2x-4) > \frac{18}{3}[/tex]

[tex]-2x-4 > 6[/tex]

4 is being subtracted from -2x. The inverse operation of subtraction is addition. Add 4 to both sides of the inequality.

[tex]-2x-4+4 > 6+4 \\[/tex]

[tex]-2x > 10[/tex]

x is being multiplied by -2. The inverse operation of multiplication is division. Divide both sides by -2.

[tex]\frac {-2x}{-2} > \frac {10}{-2}[/tex]

[tex]x> \frac {10}{-2}[/tex]

Since we divided by a negative number, the inequality sign must be flipped.

[tex]x< \frac{10}{-2}[/tex]

[tex]x < -5[/tex]

Answer:

31.25

Step-by-step explanation:

Divide 250 by 8=31.25

Answer:

79 inches

Step-by-step explanation:

1 foot equals 12 inches

6 feet = 6*12 = 72 inches

72+7=79

79 inches

Answer:

The answer is C

Step-by-step explanation:

(I'm not completely sure)

Using the together rate, it is found that:

The together rate is the sum of each separate rate.

In this problem, we have that:

Applying the together rate:

[tex]\frac{1}{x} + \frac{1}{x + 3} = \frac{1}{2}[/tex]

[tex]\frac{x + 3 + x}{x(x + 3)} = \frac{1}{2}[/tex]

[tex]4x + 6 = x^2 + 3x[/tex]

[tex]x^2 - x - 6 = 0[/tex]

Which is a quadratic equation with coefficients [tex]a = 1, b = -1, c = -6[/tex], hence:

[tex]\Delta = b^2 - 4ac = (-1)^2 - 4(1)(-6) = 25[/tex]

[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{1 + \sqrt{25}}{2} = 3[/tex]

[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{1 - \sqrt{25}}{2} = -2[/tex]

We are interested into the positive root, then [tex]x = 3[/tex], [tex]x + 3 = 6[/tex], which means that:

You can learn more about the together rate at https://brainly.com/question/25159431

Answer:

it'd be d: 13/50 !!

Answer:

D. 13/50

Step-by-step explanation:

0.26 ⇔ 26/100 ⇔ 13/50

Using the Central Limit Theorem, it is found that:

The sampling distribution is slightly right skewed, with mean of RM 10 and standard deviation of RM 0.5.

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

In this problem, the mean is of 10 and the standard deviation is of 2.50, hence [tex]\mu = 10, \sigma = 2.5[/tex]

Sample of 25, hence [tex]n = 25, s = \frac{2.5}{\sqrt{25}} = 0.5[/tex]

Since the underlying distribution is skewed and the sample size is less than 30, the shape of the sampling distribution is slightly right skewed.

The sampling distribution is slightly right skewed, with mean of RM 10 and standard deviation of RM 0.5.

A similar problem is given at https://brainly.com/question/25817309

Answer:

P(X ≤ 46 | X~B(821, 0.078)) = 0.00885745584

0.00885... < 0.01

The test statistic of 46 is significant

There is sufficient evidence to reject H₀ and accept H₁

Air bags are more effective as protection than safety belts

Step-by-step explanation:

821 crashes

46 hospitalisations where car has air bags

7.8% or 0.078 probability of hospitalisations in cars with automatic safety belts

α = 0.01 or 1% ← level of significance

One-tailed test

We are testing whether hospitalisations in cars with air bags are less likely than in a car with automatic safety belts;

The likelihood of hospitalisation in a car with automatic safety belts, we are told, is 7.8% or 0.078;

So we are testing if hospitalisations in cars with air bags is less than 0.078;

So, firstly:

Let X be the continuous random variable, the number of hospitalisations from a car crash with equipped air bags

X~B(821, 0.078)

Null hypothesis (H₀): p = 0.078

Alternative hypothesis (H₁): p < 0.078

According to the information, we reject H₀ if:

P(X ≤ 46 | X~B(821, 0.078)) < 0.01

To find P(X ≤ 46) or equally P(X < 47), it could be quite long-winded to do manually for this particular scenario;

If you are interested, the manual process involves using the formula for every value of x up to and including 46, i.e. x = 0, x = 1, x = 2, etc. until x = 46, the formula is:

[tex]P(X = r) = nCr * p^{r} * (1 - p)^{n - r}[/tex]

You can find binomial distribution calculators online, where you input n (i.e. the number of trials or 821 in this case), probability (i.e. 0.078) and the test statistic (i.e. 46), it does it all for you, which gives:

P(X ≤ 46 | X~B(821, 0.078)) = 0.00885745584

Now, we need to consider if the condition for rejecting H₀ is met and recognise that:

0.00885... < 0.01

There is sufficient evidence to reject H₀ and accept H₁.

To explain what this means:

The test statistic of 46 is significant according to the 1% significance level, meaning the likelihood that only 46 hospitalisations are seen in car crashes with air bags in the car as compared to the expected number in car crashes with automatic safety belts is very unlikely, less than 1%, to be simply down to chance;

In other words, there is 99%+ probability that the lower number of hospitalisations in car crashes with air bags is due to some reason, such as air bags being more effective as a protective implement than the safety belts in car crashes.

Answer:

A year but -1.

Step-by-step explanation:

52x7=364.

Hope this helps!

Answer:

there are 364 days in 52 weeks.

Step-by-step explanation:

To find out how many days are in 52 weeks you have to multiply the amount of days there are in a week by 52, there are 7 days in a week and 7 times 52 is 364 so the answer is 364

Answer:

  see attached

Step-by-step explanation:

The one that matches the triangle shown in the attachment has the given vertices.

Answer:

Step-by-step explanation:

Let x be the adjacent side length in cm

opposite side is x + 2 cm

hypotenuse is x + 4 cm

x² + (x + 2)² = (x + 4)²

x² + (x² + 4x + 4) = (x² + 8x + 16)

x² - 4x - 12 = 0

(x - 6)(x + 2) = 0

so either

x - 6 = 0    x = 6

or

x + 2 = 0    x = -2

positive answer is x = 6 as negative length does not make sense

opposite side is 6 + 2 = 8

hypotenuse is 6 + 4 = 10

perimeter is 6 + 8 + 10 = 24 cm

Answer:

First, let's look at some polynomials of even degree (specifically, quadratics in the first row of pictures, and quartics in the second row) with positive and negative leading coefficients:❤

Step-by-step explanation:

12/14= 85.7143% 19/24= 79.1667%

Step-by-step explanation:

1. KOL = 90

2.KLO = 25

3.NL= 30

4.KL = 17

workings

1.for angle

KOL =90 : the diagonals of rhombus are perpendicular to each other

2. angle LKO + angle KLO + angle KOL =180 : angles of triangle are supplementary(add to 180)

65+ KLO + 90 =180

KLO +155

KLO = 180 - 155

KLO = 25

3. NL = NO + LO: diagonals of the rhombus bisect each other

NL = 15 +15

NL = 30

4. Cos 25 = 15/KL

multiply by KL on both sides

KL × Cos 25 =15

divide by cos 25 on both sides

KL = 17

Answer:

  x > 23/6

Step-by-step explanation:

Solve this one the same way you would a 2-step linear equation.

  6x +3 > 26 . . . . . given

  6x > 23 . . . . . . . . subtract the unwanted constant from both sides (step 1)

  x > 23/6 . . . . . . . .divide both sides by the coefficient of x (step 2)

__

Additional comment

If the coefficient of the variable in a 2-step linear inequality is negative, then the inequality symbol must be reversed when dividing by that negative number.

Correction:

5+13+21+...+181

First term = 5

Common difference = 13-5 = 8

Last term = an = 181

⇛a+(n-1)d = 181

⇛5+(n-1)(8) = 181

⇛ 5+8n-8 = 181

⇛ 8n-3 = 181

⇛ 8n = 181+3

⇛ 8n = 184

⇛n = 184/8

⇛ n = 23

Sum of the first n terms = Sn = (n/2)(a+an)

Sum of 23 terms = S 23

⇛(23/2)(5+181)

⇛ (23/2)(186)

⇛23×93

⇛2139

the inequality is 8 (w+18) ≤ 19

Answer: -15.625

Step-by-step explanation:

Let w represent the number:

8 (w + 18) ≤ 19

[tex]\frac{8\left(w+18\right)}{8}\le \frac{19}{8}[/tex]

[tex]w+18\le \frac{19}{8}[/tex]

[tex]w+18-18\le \frac{19}{8}-18[/tex]

[tex]w\le \:-\frac{125}{8}[/tex]

-125/8 or -15.625

Check:

[tex]8\left(-15.625+18\right)\le \:19[/tex]

[tex]8\cdot \:2.375 \leq 19[/tex]

[tex]19 \leq 19[/tex]

Therefore, the number is -15.625

Answer:

To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. For example 0.54+0.27 and 0.24 +0.57, If we know the value of our variables, we can replace the variables with their values and then evaluate the expression.

hope this helps.