The zeros in a function are where it passes through the..?
To find the zeros, set the equation equal to [Blank] then solve for x!

Answer:

5:05 PM

Step-by-step explanation:

Use a time calculator.

Answer:5:05pm

Step-by-step explanation:

It might be easier to split up the 5 hours and 35 min in minutes and hours

11:30 + 5 hours = 4:30pm

There is still 35 minutes left.

4:30 + 35 min = 5:05pm

∴, Christine finished shopping at 5:05pm

The length of side LJ is equal to 11.48 units.

In Mathematics and Geometry, two (2) triangles are only similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Based on the diagram, we can logically deduce the following proportion based on the congruent sides:

XY/JK = YZ/KL = ZX/LJ

8.7/12.18 = 8.2/LJ = 7.8/KL

By cross-multiplying and solving for the length of side LJ, we have the following:

LJ = (12.18 × 8.2)/8.7

LJ = 11.48 units.

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The probability of either event E or event F occurring, when E and F are mutually exclusive, is 0.85.

If E and F are mutually exclusive events, it means that they cannot occur simultaneously. In such cases, the probability of either event E or event F occurring is the sum of their individual probabilities.

Given that P(E) = 0.34 and P(F) = 0.51, we can calculate the probability of E or F, denoted as P(E or F), as:

P(E or F) = P(E) + P(F)

Substituting the given values, we have:

P(E or F) = 0.34 + 0.51

Calculating the sum, we find:

P(E or F) = 0.85

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The trigonometric ratios for tangent indicates that the height of the kite, where the distance between the observers is 500 m, and the angle of elevation are 30° and 20° is h ≈ 492.4 meters

Trigonometric ratios are mathematical functions that express the relationships between an interior angle of a right triangle and two of the sides of the triangle.

The distance between the two observers = 500 m

The angle of observation of the kite by each of the two observers = 30° and 20°

Let h represent the height of the kite, and let x represent the horizontal distance from the kite to the closer observer (The observer observing with an angle of elevation of 30°), we get;

The horizontal distance from the kite to the other observer = x + 500

Therefore, according to the trigonometric ratios for tangent;

tan(20°) = h/(x + 500)

tan(30°) = h/x

h = x × tan(30°)

Therefore;

tan(20°) = (x × tan(30°))/(x + 500)

(x + 500) × tan(20°) = x × tan(30°)

(x + 500) × 0.36397 = x × (1/(√3))

0.36397·x + 500 × 0.36397 = x/√3

x/√3 - 0.36397·x = 500 × 0.36397 = 181.985

x·(1/√3 - 0.36397) = 181.985

x = 181.985/((1/√3 - 0.36397))

h = 181.985/((1/√3 - 0.36397)) × tan(30°)

h = 181.985/((1/√3 - 0.36397)) × (1/√3) ≈ 492.4

The height of the kite, h ≈ 492.4 meters

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The maximum number of points that may not be on the line is given as follows:

A. 6.

To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in a linear regression calculator.

When we insert the points on a calculator, we get a linear function that is obtained using the mean and sum of squares of the points. This means that the line has on average the least distance to the points, but it can happen that none of the points is exactly on the line.

Hence option A is the correct option in the context of this problem.

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To minimize the amount of material used for the box, we want to minimize its surface area. Since the base of the box is a square, let's denote its side length as s. Then, the height of the box can be expressed as 7500/s^2, using the given volume.

Using this information, we can express the surface area of the box as a function of s: A(s) = 2s^2 + 4sh, where h is the height of the box. Substituting 7500/s^2 for h, we get A(s) = 2s^2 + 4(7500/s^2)s.

To find the minimum amount of material used, we need to find the value of s that minimizes A(s). We can do this by finding the critical points of A(s) and then using the second derivative test to determine if they correspond to a minimum. Taking the derivative of A(s) and setting it equal to zero, we get:

A'(s) = 4s - 30000/s^3 = 0

Solving for s, we get s = 15∛125 ≈ 12.247.

To confirm that this value corresponds to a minimum, we take the second derivative of A(s) and evaluate it at s = 12.247:

A''(s) = 4 + 90000/s^4

A''(12.247) ≈ 0.143

Since A''(12.247) is positive, we can conclude that s = 12.247 corresponds to a minimum of A(s). Therefore, the of the box should be approximately 12.247 cm by 12.247 cm by 41.666 cm to minimize the amount of material used.

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answer

(1.2, 1) if its asking what i think it is

Step-by-step explanation:

Answer:

x=9

Step-by-step explanation:

Since x is a midsegment this means that it bisects the side with a length of 16. Now using ratio and proportion between the large triangle and the small triangle to find the length of x you have to do

18/16=x/(16/2)

16x=18(8)

x= 144/16

x=9

The distance left to hike by Cassius is equal to 1.44 miles . Dana hiked 3.5986 miles

We are given that Cassie hiked 4 tenths of a 4.7-mile trail and  Dana was 1.6 miles ahead of Cassie.

Since Cassius walked 6/10th of the trail of 3.6 miles.

Part of the trail remaining = 1 - 6/10 = 4/10 = 2/5

Distance remaining will be  2/5 of 3.6 miles

= 1.44 miles.

Hence distance left to hike by Cassius = 1.44 miles  

b. Total distance by which Dana was ahead of Cassius =  1.6miles.

Distance left to hike by Dana= 1.44 miles - 1.6 miles = 0.0014 miles.

so, the distance hiked by Dana= 3.6 miles - 0.0014 miles = 3.5986 miles.

Dana hiked 3.5986 miles.

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Answer: To determine the time it would take to save $3400 in an account with a 0.12% interest rate compounded continuously to end up with $5000, we can use the continuous compound interest formula:

A = Pe^(rt)

Where:

A = the final amount in the account ($5000 in this case)

P = the initial amount in the account ($3400 in this case)

e = the mathematical constant e (approximately equal to 2.71828)

r = the annual interest rate (0.12% = 0.0012 as a decimal)

t = the time in years

We can rearrange this formula to solve for t:

t = ln(A/P) / r

Substituting the values given, we get:

t = ln(5000/3400) / 0.0012

t = 28.58 years (rounded to two decimal places)

Therefore, it would take approximately 28.58 years to save $3400 in an account with a 0.12% interest rate compounded continuously to end up with $5000.

Step-by-step explanation:

The angle of 53° is equals to,

The given angle = 53°

        the equivalent angle in the second quadrant = 180° - 53° = 127°.

        equivalent angle in third quadrant = 180° + 53° = 233°.

        equivalent angle in fouth quadrant = 360° - 53° = 307°.

From the above analysis, we have found the equivalent angles in all quadrants.

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-15 is the value of the variable x in the given equation -3x+x-5= 25

The given equation is -3x+x-5= 25

Minus three times of x plus x minus five equal to twenty five

x is the variable in the equation

Minus and plus are the operators

Combine the like terms in the equation

-2x-5=25

Add 5 on both sides

-2x=30

x=-15

Hence, the value of x in the equation is -15

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b)i) The curve that matches y = x² - 2x - 3 is the middle one, which is a parabola opening upward. b)ii)  we can estimate that y(2.5) ≈ y(2) + 3/2 = -3 + 3/2 = -1.5. b)iii) the only value of x when y = 1 is x = 2.

a)

| x | y

| -3 | 12

| -2 | 1

| -1 | -4

| 0 | -3

| 1 | -2

| 2 | -3

| 3 | 0

b) i) The curve that matches y = x² - 2x - 3 is the middle one, which is a parabola opening upward.

ii) To estimate the value of y when x = 2.5, we can use the values of y when x = 2 and x = 3 to find the average rate of change, and then add or subtract that from the value of y when x = 2 or x = 3, respectively.

Using x = 2 and x = 3, we have:

Average rate of change = (y(3) - y(2)) / (3 - 2) = 3

So we can estimate that y(2.5) ≈ y(2) + 3/2 = -3 + 3/2 = -1.5.

iii) To find the values of x when y = 1, we can set y = 1 in the equation y = x² - 2x - 3 and solve for x:

x² - 2x - 3 = 1

x² - 2x - 4 = 0

(x - 2)² = 0

x - 2 = 0

x = 2

So the only value of x when y = 1 is x = 2.

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Answer: $3.32

Step-by-step explanation:

-0.3853 = (x - 3.4) / 0.2

Solving for x, we get:

X = 3.32

Therefore, the price for which only 35% of milk vendors is lower than $3.32.

so hmmm let's call them P(2, 4) and Q(10, 8)

[tex]\textit{internal division of a segment using a fraction}\\\\ P(\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad Q(\stackrel{x_2}{10}~,~\stackrel{y_2}{8})~\hspace{8em} \frac{1}{4}\textit{ of the way from P to Q} \\\\[-0.35em] ~\dotfill[/tex]

[tex](\stackrel{x_2}{10}-\stackrel{x_1}{2}~~,~~ \stackrel{y_2}{8}-\stackrel{y_1}{4})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment PQ}}}{\left( 8 ~~,~~ 4 \right)} \\\\[-0.35em] ~\dotfill\\\\ \left( \stackrel{x_1}{2}~~+~~\frac{1}{4}(8)~~,~~\stackrel{y_1}{4}~~+~~\frac{1}{4}(4) \right) \implies \boxed{(4~~,~~5)}[/tex]

Janet's Athletic Company can ship 15 basketballs in the round containers with a volume of 208,592.

To figure out how many basketballs Janet's Athletic Company can ship, we need to divide the volume of the round containers by the volume of each basketball. So we can set up the following equation:
Number of basketballs = Volume of round containers / Volume of each basketball
Plugging in the given values, we get:
Number of basketballs = 208,592 / 13906
Simplifying the division, we get:
Number of basketballs = 15
Therefore, Janet's Athletic Company can ship 15 basketballs in the round containers with a volume of 208,592.

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The total balance in the savings account after 10 years will be $2,187.48.

The formula accrued amount in a compounded interest is expressed as;

[tex]A = P(1 + \frac{r}{n} )^{(n*t)}[/tex]

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given that:

First, convert R as a percent to r as a decimal

r = R/100

r = 2.1/100

r = 0.021

Now, plug the values into the above formula and simplify.

[tex]A = P(1 + \frac{r}{n} )^{(n*t)}\\\\A = 1,777(1 + \frac{0.021}{1} )^{(1*10)}\\\\A = 1,777(1 +0.021 )^{(10)}\\\\A = 1,777(1.021 )^{(10)}\\\\A = 2,187.48[/tex]

Therefore, the accrued amount is $2,187.48.

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The volume of the cube is greater than 5.4 cubic inches.

The volume of a cube of side length a is given by the cube of the side length, as follows:

V = a³.

The side length in the context of this problem is given as follows:

a = 5.4 in.

Hence the volume of the cube is given as follows:

V = 5.4³

V = 157.5 cubic inches.

(to obtain the volume of the cube, we apply the formula obtaining the cube of the side length).

157.5 > 5.4, hence the volume of the cube is greater than 5.4 cubic inches.

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The probabilities are given as follows:

The parameters that are needed to calculate a probability are given as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

Out of the 12 regions, 4 are unshaded, hence the probability is given as follows:

P(unshaded) = 4/12 = 1/3 = 0.33 = 33%.

Out of the 12 regions, 4 are even and less than 10, hence the probability is given as follows:

P(even and less than 10) = 4/12 = 1/3 = 0.33 = 33%.

The spinner is given by the image presented at the end of the answer.

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The general fertility rate refers to the number of live births reported in an area during a given time interval divided by the number of women age 15 to 44 years in the area is false

The general fertility rate refers to the number of live births reported in an area during a given time interval per 1,000 women of reproductive age (usually defined as 15 to 44 years old) in the same area.

Therefore, it is a rate or a ratio that expresses the number of births in relation to the number of women of reproductive age in a population.

Hence, the statement is False that the general fertility rate refers to the number of live births reported in an area during a given time interval divided by the number of women age 15 to 44 years in the area is false

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Therefore, the probability that the sample mean cholesterol level is less than 190 is approximately 0.23%.

We can use the central limit theorem to approximate the distribution of the sample mean cholesterol level as normal with a mean of 202 and a standard deviation of 41/sqrt(100) = 4.1.

To find the probability that the sample mean cholesterol level is less than 190, we can standardize the sample mean using the formula:

z = (x - mu) / (sigma / sqrt(n))

where x is the sample mean, mu is the population mean, sigma is the population standard deviation, and n is the sample size.

Plugging in the values, we get:

z = (190 - 202) / (4.1) = -2.93

Now we can use a standard normal distribution table or calculator to find the probability that a standard normal random variable is less than -2.93. The probability is approximately 0.0023 or 0.23%.

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The null hypothesis for the single factor ANOVA states that all means are equally true.

The null hypothesis for a single-factor ANOVA (analysis of variance) states that all means are equal.

The alternative hypothesis, on the other hand, suggests that at least one of the means is different from the others.

The purpose of the ANOVA test is to determine whether there is sufficient evidence to reject the null hypothesis and conclude that there are significant differences between the means. A statistical formula used to compare variances across the means (or average) of different groups.

Hence, the statement is true .

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The probability of having both lab work and a referral during a visit to a primary care physician's office is 0.16 or 16%.

To find the probability of having both lab work and a referral, we can use the formula P(A and B) = P(A) + P(B) - P(A or B), where A and B are events and P is the probability of those events occurring.

Let A be the event of having lab work and B be the event of having a referral.

We know that P(A) = 0.41, P(B) = 0.53, and P(neither A nor B) = 0.21.

To find P(A or B), we can use the formula P(A or B) = P(A) + P(B) - P(A and B). We don't know P(A and B), but we can find it by using the fact that P(neither A nor B) = 0.21:

P(A or B) = P(A) + P(B) - P(A and B)
1 - P(neither A nor B) = P(A) + P(B) - P(A and B)
1 - 0.21 = 0.41 + 0.53 - P(A and B)
0.78 = 0.94 - P(A and B)
P(A and B) = 0.16

Therefore, the probability of having both lab work and a referral is 0.16.


The probability of having both lab work and a referral during a visit to a primary care physician's office can be found using the formula P(A and B) = P(A) + P(B) - P(A or B). Given that the probability of having lab work is 0.41, the probability of having a referral is 0.53, and the probability of having neither is 0.21, we can solve for P(A and B) and get a probability of 0.16. This means that there is a 16% chance of a patient having both lab work and a referral during their visit.


In conclusion, the probability of having both lab work and a referral during a visit to a primary care physician's office is 0.16 or 16%. This calculation was done using the formula P(A and B) = P(A) + P(B) - P(A or B), with the probabilities of having lab work, a referral, and neither being given.

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Answer:

9.25 inches

Step-by-step explanation:

9.25 inches

The final temperature is 165 degree F.

Given that,

Ta = the temperature surrounding the object = 69ºF

T₀ = the initial temperature of the object = 203ºF

t = 1.5 min

T after 1.5 min = 185ºF

We know the temperature equation,

T = [tex]T_{\alpha}[/tex] + [tex](T_{0} - T_{\alpha })e^{-kt}[/tex]

Substitute the values,

185 = 69 +  (203 - 69)[tex]e^{-1.5k}[/tex]

solving it we get

k = 0.077

To find the Fahrenheit temperature of the cup of water, to the nearest degree, after 4. minutes.

Substitute into the formula and compute:

T = 69 +  (203 - 69)[tex]e^{-(0.75)(4.5)}[/tex]

Hence,

T = 165 degree F.

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The distance across the lake PQ will be 496.8 meters.

Given that:

Sides, OS = 210 m, SQ = 70 m, and RS = 124.2 m

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The distance across the lake PQ is calculated as,

PQ / RS = OQ / SQ

PQ / 124.2 = (210 + 70) / 70

PQ / 124.2 = 280 / 70

PQ = 496.8 m

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The length of the arc is approximately 4.5 to the nearest 10th.

To find the length of the arc intercepted by an angle in a circle, we can use the formula:

Arc length = radius × angle (in radians)

In this case, the radius is 4.5, and the angle is 1 radian. So, we can calculate the arc length as follows:

Arc length = 4.5 × 1 ≈ 4.5

Therefore, the length of the arc is approximately 4.5 to the nearest 10th.

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Answer:

a) 1 : 3 and 1 : 27. b) 1728 inches³

Step-by-step explanation:

a) if ratio of areas is 1:9, then the ratio of lengths is √1 : √9 = 1:3

ratio of volumes is 1³ : 3³ = 1 : 27

b) volume of smaller = 64.

ratio of volumes = 1 : 27

volume of larger sphere = 27 X 64 = 1728 (inches³)

Yes, it is possible to solve x(t) for t and substitute it into y(t) to eliminate the parameter t and write it as a rectangular equation with x and y instead.

Starting with the given equation:

x(t) = 0.5507t^2 - 1.5393t - 86.1

To solve for t, we can use the quadratic formula:

t = [-(-1.5393) ± sqrt((-1.5393)^2 - 4(0.5507)(-86.1))]/(2(0.5507))

Simplifying the equation:

t = [1.5393 ± sqrt(1.5393^2 + 190.2122)]/1.1014

t = [1.5393 ± 13.9769]/1.1014

t = -11.098 or 25.682

Since we're interested in the positive value of t, t = 25.682.

Now, substituting t = 25.682 into y(t):

y(t) = 0.5054t - 78.9

y(25.682) = 0.5054(25.682) - 78.9

y(25.682) = 1.504

Therefore, the rectangular equation for the given parametric equations is:

x = 0.5507t^2 - 1.5393t - 86.1

y = 0.5054t - 78.9

Substituting t = 25.682:

x = 358.6

y = 1.504

So the rectangular equation is:

(x, y) = (358.6, 1.504)

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