20.There is an 80% chance David will eat a healthy breakfast and a 25% chance that it will rain. If these events are independent , what is the probability that David will eat a healthy breakfast or that it will rain A.20% B.80% C.85% D.95% E.105%

The degrees of freedom (df) value for a chi-square test for independence is calculated using the formula: df = (number of columns - 1) x (number of rows - 1).

The degrees of freedom (df) value for a chi-square test for independence when both variables are classified into two categories can be calculated using the formula:

df = (number of columns - 1) x (number of rows - 1)

For example, if we have a contingency table with 2 columns and 2 rows, the df value would be:

df = (2 - 1) x (2 - 1) = 1 x 1 = 1

Answer:

230.

Step-by-step explanation:

You have a 50% chance to get heads or tails. So that's half of 490, which is 245. It says estimate, so that means a relative guess. 230 would be the closest.

Final answer:

To estimate the number of times a coin flipped 490 times lands on heads, one should expect approximately half of the flips to be heads, which is about 245. Thus, option B. 230 is the closest estimation.

Explanation:

The question deals with the probability of outcomes when flipping a coin multiple times. When you flip a coin, the probability of it landing on heads is 50 percent each time, irrespective of previous outcomes. Thus, if you flip a coin 490 times, a good estimate for the number of times it will land on heads is roughly half of 490, which is 245. Therefore, the best estimate from the given options would be B. 230, as it is the closest to 245.

Answer:

  -5/4

Step-by-step explanation:

See the attachment for rise and run lines. The slope is the ratio ...

   slope = rise / run = -5/4

In mathematics, 'rise' and 'run' are used to find the slope of a line. They represent vertical and horizontal distances respectively between two points. Slope, represented as 'm' is calculated as 'rise/run' which gives the ratio of the vertical change to the horizontal change.

In Mathematics, specifically in Algebra and Geometry, the terms 'rise' and 'run' refer to the vertical and horizontal distances between two points on a line, respectively. In the context of a line on a graph, the 'run' corresponds to the difference in the x-values of the points (horizontal change), while the 'rise' corresponds to the difference in the y-values of the points (vertical change). These terms are crucial when calculating the slope of a line.

The slope of a line, also often represented by the letter 'm', is computed as 'rise/run', giving us the ratio of the vertical change to the horizontal change between two points on the line. If for instance, the rise is 4 units and the run is 2 units, your slope or 'm' would be 4/2 which simplifies to 2. This means that for every step you move horizontally (run), you move two steps vertically (rise).

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Answer:

a and b both are true.

Step-by-step explanation:

Given : A coin is tossed 10 times.

To find : True or false, and explain ?

Solution :

(a) The chance of getting 10 heads in a row is [tex]\frac{1}{1024}[/tex]

Coin has two face head and tail.

The probability of getting head is [tex]P(H)=\frac{1}{2}[/tex]

The probability of getting 10 heads in a row is

[tex]P=(P(H))^{10}[/tex]

[tex]P=(\frac{1}{2})^{10}[/tex]

[tex]P=\frac{1}{1024}[/tex]

The chance of getting 10 heads in a row is [tex]\frac{1}{1024}[/tex] is true.

(b) Given that the first 9 tosses were heads, the chance of getting 10 heads in a row is [tex]\frac{1}{2}[/tex].

The probability of getting 10 heads in a row is [tex]P_1=(\frac{1}{2})^{10}[/tex]

The probability of getting 9 tosses were heads is [tex]P_2=(\frac{1}{2})^{9}[/tex]

Given that the first 9 tosses were heads, the chance of getting 10 heads in a row is given by,

[tex]P=\frac{P_1}{P_2}[/tex]

[tex]P=\frac{(\frac{1}{2})^{10}}{(\frac{1}{2})^{9}}[/tex]

[tex]P=(\frac{1}{2})^{10-9}[/tex]

[tex]P=\frac{1}{2}[/tex]

Given that the first 9 tosses were heads, the chance of getting 10 heads in a row is [tex]\frac{1}{2}[/tex] is true.

(a) True: The chance of getting 10 heads in a row is [tex]\( \frac{1}{1024} \)[/tex].

(b) True: Given 9 heads, the chance of the 10th being heads remains [tex]\( \frac{1}{2} \).[/tex]

Step 1:

(a) The chance of getting 10 heads in a row:

The probability of getting heads on a single toss of a fair coin is [tex]\( \frac{1}{2} \).[/tex]

Since each toss is independent, the probability of getting 10 heads in a row is calculated by multiplying the individual probabilities:

[tex]\[ \left( \frac{1}{2} \right)^{10} = \frac{1}{1024} \][/tex]

Step 2:

(b) Given that the first 9 tosses were heads, the chance of getting 10 heads in a row:

Since each toss is independent, the probability of getting heads on the 10th toss is still  [tex]\( \frac{1}{2} \).[/tex]

So, the chance of getting 10 heads in a row given the first 9 were heads remains [tex]\( \frac{1}{2} \).[/tex]

Therefore, the calculations support the statements:

(a) The chance of getting 10 heads in a row is indeed [tex]\( \frac{1}{1024} \)[/tex].

(b) Given the first 9 tosses were heads, the chance of getting 10 heads in a row is still [tex]\( \frac{1}{2} \).[/tex]

Answer:

C. Savings instrument that requires a desposit for a period of time during which there is a penalty for withdrawals.

Step-by-step explanation:

A Certificate of Deposit is a financial savings product offered by banks. A Certificate of Deposit, also known as a CD, can be obtained from a bank or a credit union.

CDs have a greater interest rate return than savings accounts due the conditions that savings from a CD cannot be withrawn for a fixed period of time. The higher the return the longer the period the savings cannot be withdrawn or the higher the intital investment.

CDs are insured by the Federal Deposit Insurance Corporation (FDIC) and if savings are not needed for a known period of time offer a better return than a savings account.

Answer:

C. Savings instrument that requires a desposit for a period of time during which there is a penalty for withdrawals.

Answer:

Sample size should be atleast 617

Step-by-step explanation:

given that a 95% confidence interval for the mean of a population is to be constructed and must be accurate to within 0.3 unit.

i.e. margin of error <0.3

Std devition sample = 3.8

For 95% assuming sample size large we can use z critical value

Z critical = 1.96

we have

[tex]1.96 * std error <0.3\\1.96(\frac{3.8}{\sqrt{n} } )<0.3\\\sqrt{n} >24.83\\n>616.3634[/tex]

Sample size should be atleast 617 to get an accurate margin of error 0.3

To construct a 95% confidence interval with an accuracy of 0.3 units, the smallest sample size (n) is 25.

To construct a 95% confidence interval with an accuracy of 0.3 units, we need to determine the sample size (n). We can use the formula:

n = (Z * σ) / E

Where Z is the Z-score corresponding to the desired confidence level (in this case, 95% corresponds to a Z-score of 1.96), σ is the preliminary sample standard deviation (3.8), and E is the desired accuracy (0.3).

Substituting the values into the formula:

n = (1.96 * 3.8) / 0.3 = 24.8

Rounding up to the nearest whole number, the smallest sample size n that provides the desired accuracy is 25.

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Answer:

a) [tex]z_{\alpha/2}=-1.51[/tex] and [tex]z_{\alpha/2}=1.51[/tex]

b) [tex]t_{\alpha/2}=-1.89[/tex] and [tex]t_{\alpha/2}=1.89[/tex]

c) [tex]t_{\alpha/2}=-2.11[/tex]

d) [tex]z_{\alpha/2}=-1.75[/tex] and [tex]z_{\alpha/2}=1.75[/tex]

Step-by-step explanation:

Part a

On this case the confidence is 87% or 0.87 so the significance level is [tex]\alpha=1-0.87=0.13[/tex] and [tex]\alpha/2 =0.065[/tex]. On this case we can assume that is a bilateral test or a confidence interval so we will have two critical values.

We need values a,b on the normal standard distribution such that:

[tex]P(Z<a)=0.065[/tex] or [tex]P(Z>b)=0.065[/tex] and in order to find it we can use the following code in excel:

"NORM.INV(0.065,0,1)" or "NORM.INV(1-0.065,0,1)", and we see that the critical values [tex]z_{\alpha/2}=-1.51[/tex] and [tex]z_{\alpha/2}=1.51[/tex]

Part b

On this case the confidence is 92% or 0.92 so the significance level is [tex]\alpha=1-0.92=0.08[/tex] and [tex]\alpha/2 =0.04[/tex]. On this case we can assume that is a bilateral test or a confidence interval so we will have two critical values.

First we need to calculate the degrees of freedom given by:

[tex]df=n-1=15-1=14[/tex]

We need values b,c on the t distribution with 14 degrees of freddom such that:

[tex]P(t_{(14)}<b)=0.04[/tex] or [tex]P(t_{(14)}>c)=0.04[/tex] and in order to find it we can use the following code in excel:

"T.INV(0.04,14)" or "T.INV(1-0.04,14)", and we see that the critical values [tex]t_{\alpha/2}=-1.89[/tex] and [tex]t_{\alpha/2}=1.89[/tex]

Part c

The significance level is [tex]\alpha=0.025[/tex] and is a left tailed test. On this case we know that is a left tailed test so then we have just one critical value.

First we need to calculate the degrees of freedom given by:

[tex]df=n-1=18-1=17[/tex]

We need a value c on the t distribution with 17 degrees of freddom such that:

[tex]P(t_{(17)}<c)=0.025[/tex], and in order to find it we can use the following code in excel:

"T.INV(0.025,17)", and we see that the critical values [tex]t_{\alpha/2}=-2.11[/tex]

Part d

The significance level is [tex]\alpha=0.08[/tex] and [tex]\alpha/2 =0.04[/tex]. On this case we know that w ehave a two tailed proportion test, so we will have two critical values.

We need values a,b on the normal standard distribution such that:

[tex]P(Z<a)=0.04[/tex] or [tex]P(Z>b)=0.04[/tex] and in order to find it we can use the following code in excel:

"NORM.INV(0.04,0,1)" or "NORM.INV(1-0.04,0,1)", and we see that the critical values [tex]z_{\alpha/2}=-1.75[/tex] and [tex]z_{\alpha/2}=1.75[/tex]

a. The critical value z????/2 for a level of confidence of 87% is approximately 1.475. b. The critical t-value t????/2 for a 92% confidence level and n = 15 is approximately 1.761. c. The critical value for a left-tailed test at α = 0.025 and n = 18 is approximately -2.101. d. The critical value for a two-tailed test of a population proportion with α = 0.08 is approximately 1.755.

a. To find the critical value z????/2 for a level of confidence of 87%, we need to find the z-score that leaves an area of 0.87 in the center. This means the area in each tail is (1 - 0.87) / 2 = 0.065. Using a z-table or calculator, the critical value is approximately 1.475.

b. For a 92% confidence level and a sample size of 15, we need to find the critical t-value t????/2. First, we determine the degrees of freedom, which is n - 1 = 15 - 1 = 14. Using a t-table or calculator, the critical t-value is approximately 1.761.

c. For a left-tailed test at the α = 0.025 level of significance and a sample size of 18, we need to find the critical value. Since the level of significance is α = 0.025, the area in the left tail is 0.025. Using a t-table or calculator, the critical value is approximately -2.101.

d. For a two-tailed test of a population proportion with α = 0.08, we need to find the critical value. Since we have a two-tailed test, we divide α by 2 to get 0.08 / 2 = 0.04. Using a z-table or calculator, the critical value is approximately 1.755.

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Answer:

External stakeholder.

Step-by-step explanation:

Radio Plus is invested in this relationship because it generates most of its revenue from advertising Organic Food's products.

In this scenario, Radio Plus is Organic Food Inc.'s - external stakeholder.

External stakeholders are those individuals or companies that do not lie within a business itself, but these care about the business and are affected by the business's performance.

Answer:

  160°

Step-by-step explanation:

The corresponding exterior angle is 180°-140° = 40°. When the polygon has 2n sides, that angle will be cut in half to 20°. The interior angle of that polygon will be 180°-20° = 160°.

_____

The exterior angles always sum to 360°. Since their sum is a constant, doubling the number of them will cut their measure in half.

To find the size of each interior angle in a regular polygon with 2n sides, when n sides gives 140° each, we use the interior angle formula (n-2) * 180 / n. First, we find n using 140 = (n-2) * 180 / n and substitute n into ((2*n) - 2) * 180 / (2*n) for the result.

The size of each interior angle in a regular polygon is calculated using the formula (n-2) * 180 / n, where n is the number of sides. Given that a polygon with n sides has an interior angle of 140°, we can use this formula to calculate the size of each interior angle in a regular polygon with 2*n sides. The calculation would be: ((2*n) - 2) * 180 / (2*n).

Therefore, to calculate the size of each interior angle in a regular polygon with 2*n sides - if n sides gives 140° each, we must first calculate n using 140 = (n-2) * 180 / n and then substitute n in ((2*n) - 2) * 180 / (2*n) to get the result.

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Answer:

5 i)  Space occupied by 1 ball = 137.26 cubic centimeters

5 ii)  Space occupied by 6 tennis balls =  823.56 cubic centimeters

6 i)  19.2 centimeters

6 ii)  12.8 centimeters

6 iii) 6.4 centimeters

6 iv)  1572.86 cubic centimeters

7.  749.3 cubic centimeters

Step-by-step explanation:

5.

i)

A tennis ball is in a shape of a sphere. The space occupied by 1 tennis ball is the volume of a sphere. The formula is:

[tex]V=\frac{4}{3}\pi r^3[/tex]

Where

V is the volume and r is the radius (half of diameter)

Given diameter is 6.4 , the radius would be:

r = 6.4/2 = 3.2

Now, we substitute and find the volume:

[tex]V=\frac{4}{3}\pi r^3\\V=\frac{4}{3}\pi (3.2)^3\\V=137.26[/tex]

Space occupied by 1 ball = 137.26 cubic centimeters

ii)

We found space occupied by 1 ball, so space occupied by 6 balls would be 6 times that. So that would be:

Space occupied by 6 tennis balls = 137.26 * 6 = 823.56 cubic centimeters

6.

i)

The length of the box would be 3 diameters lined up. Since the length comprises of 3 balls side by side, we can say that 6 diameters would make up the length of the box, so:

diameter = 6.4

3 diameters = 6.4 * 3 = 19.2 centimeters

ii)

Now, we want the width of the box. That is 2 tennis balls lined up (as seen in the picture). That would be 2 diameters. so:

diameter = 6.4

2 diameters = 6.4 * 2 = 12.8 centimeters

iii)

The height of the box would be the height of 1 balls (see pic). That would be just 1 diameter of the ball. Given:

Diameter = 6.4 cm

So,

Height = 6.4 cm

iv)

The box is a rectangular prism. Which has a capacity (volume) formula as:

Volume = length * width * height

In the first 3 parts of this problem, we found each. Let's multiply each out to find the capacity of the box.

Volume = 19.2 * 12.8 * 6.4 = 1572.86 cubic centimeters

7.

The amount of empty space in the box is the volume of the rectangular box MINUS the volume of all the 6 balls. We have already found:

Volume of Box = 1572.86

Volume of 6 balls = 823.56

Hence,

Empty Space = 1572.86 - 823.56 = 749.3 cubic centimeters

Answer:

3/5

Step-by-step explanation:

Out of the 10 times flipped, you got heads 6 times

That is 6/10 or 3/5

Answer:3/5

Step-by-step explanation:took the test and got right

Answer:

$ 55135.978

Step-by-step explanation:

At most, the present value of annuity must be paid. So we must find the present value of the annuity

Given in the problem, we have:

Periodic Payment = PMT = $10000

Rate of interest annually = i = 6.35 %= [tex]\frac{6.35}{100}[/tex]=0.0635

no. of periods= n=7

So to solve this, we need to use the present value formula:

Present Value = Periodic payment [tex]\frac{1-(1+rate.of.interest)^{-n} }{rate.of.interest}[/tex]

Present Value = PMT [tex]\frac{1-(1+i)^{-n} }{i}[/tex]

Present value = 10000[tex]\frac{1-(1+0.0635)^{-7} }{0.0635}[/tex]

Present Value =10000[tex]\frac{0.35011}{0.0635}[/tex]

Present Value =10000 (5.5135978)

Present value= $ 55135.978

Which is the amount that must be paid at most to get annuities such that $10,000 annually over the 7-year period are to be received.

You should pay approximately $55,598 for a 7-year ordinary annuity with a guaranteed 6.35% annual interest rate to receive annual payments of $10,000.

To find out how much you should pay for a 7-year ordinary annuity with a guaranteed rate of 6.35% compounded annually to receive payments of $10,000 annually, we can use the present value of an annuity formula:

PV = PMT × [(1 - (1 + r)⁻ⁿ) / r]

Substituting the values into the formula:

PV = $10,000 × [(1 - (1 + 0.0635)⁻⁷) / 0.0635]

PV = $10,000 × [(1 - (1 / (1.0635)⁷)) / 0.0635]

PV = $10,000 × [(1 - (1 / 1.545677)) / 0.0635]

PV = $10,000 × [0.353032 / 0.0635]

PV = $10,000 × 5.5598

PV ≈ $55,598

Therefore, you should pay approximately $55,598 for this annuity to receive payments of $10,000 annually over 7 years.

Answer:

Option d

Step-by-step explanation:

given that a, b, c, and d be non-zero real numbers.

[tex]ax(cx + d) = -b(cx+d) \\acx^2+x(ad+bc)+bd =0[/tex]

we can factorise this equation by grouping

[tex](acx^2+xad)+)xbc+bd) =0\\ax(cx+d) +b(cx+d) =0\\(ax+b)(cx+d) =0[/tex]

Equate each factor to 0 to get

[tex]x=\frac{-b}{a} , \frac{-d}{c}[/tex]

Ratio of one solution to another would be

[tex]\frac{-b}{a} / \frac{-d}{c} \\=\frac{ad}{bc}[/tex]

So ratio would be ad/bc

Out of the four options given, option d is equal to this

So option d is right

Answer:

There are 436937109262510348800 ways to selected 12 countries.

Step-by-step explanation:

Let [tex]x_1, x_2, x_3, x_4,x_5[/tex] the countries selected from the block of 45. For [tex]x_1[/tex] there are 45 options of countries to select. For [tex]x_2[/tex] there are 44 options of countries to select because there can be no repeated countries. With the same reasoning, for [tex]x_3[/tex] there are 43 options, for [tex]x_4[/tex] there are 42 options and for [tex]x_5[/tex] there are 41 options.

Let [tex]x_6, x_7, x_8, x_9[/tex] the countries selected from the block of 57 countries. For [tex]x_6[/tex] there are 57 options of countries to select. For [tex]x_7[/tex] there are 56 options of countries to select because there can be no repeated countries. With the same reasoning, for [tex]x_8[/tex] there are 55 options and for [tex]x_9[/tex] there are 54 options.

Let [tex]x_{10}, x_{11}, x_{12}[/tex] the countries selected from the block of 69 remain countries. For [tex]x_{10}[/tex] there are 69 options of countries to select. For [tex]x_{11}[/tex] there are 68 options of countries to select because there can be no repeated countries and for [tex]x_{12}[/tex] there are 67 options.

For find the total of options o ways to select 12 countries we multiply the above options.

[tex]45*44*43*42*41*57*56*55*54*69*68*67= 436937109262510348800[/tex]

Final answer:

The number of ways to select 12 countries from the United Nations to serve on a council is determined by calculating the combinations for each block of countries and then multiplying these values together.

Explanation:

The student question deals with determining the number of ways to select 12 countries from the United Nations to serve on a council, given specific blocks of countries to choose from. To calculate this, we use the principles of combinations, as the order of selection does not matter. The number of ways to select 5 countries from the first block of 45 is given by the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of items to choose from, k is the number of items to choose, and '!' denotes factorial. Applying this to the first block:

C(45, 5) = 45! / (5! * (45-5)!) = 1,221,759 ways

Similarly, for the second block of 57 countries, from which 4 must be chosen:

C(57, 4) = 57! / (4! * (57-4)!) = 496,674 ways

For the remaining 3 countries from the last block of 69:

C(69, 3) = 69! / (3! * (69-3)!) = 54,834 ways

To find the total number of combinations, we multiply the number of ways for each block, as each selection is independent of the others:

Total ways = C(45, 5) * C(57, 4) * C(69, 3) = 1,221,759 * 496,674 * 54,834

After calculating this product, we obtain the total number of ways to select 12 countries from the United Nations for the council.

If you go by division is is eight to nine.

Final answer:

The ratio of threatened species of animals to threatened species of plants in the United States in 2001, expressed in simplest form, is 8:9 or 8/9 after dividing both numbers by their greatest common divisor, which is 16.

Explanation:

The question asks for the ratio of threatened species of animals to threatened species of plants in the United States in 2001, expressed as a fraction in simplest form. To find the ratio, we divide the number of threatened animal species by the number of threatened plant species. The given numbers are 128 threatened animal species and 144 threatened plant species.

To simplify the ratio 128:144, we divide both numbers by their greatest common divisor (GCD). The GCD of 128 and 144 is 16. Thus, dividing both sides of the ratio by 16, we obtain:

128 ÷ 16 = 8

144 ÷ 16 = 9

The simplified form of the ratio is 8:9, or written as a fraction 8/9.

Answer:

9/49

Step-by-step explanation:

For the first die, probability of obtaining 4= 2/7

For the second die, the probability of obtaining 3= 2/7

Other outcomes for each die appear with a probability of 1/7

There are six cases of obtaining the sum of the two die as 7.

E1 = 1 and 6

E2 = 2 and 5

E3 = 3 and 4

E4 = 4 and 3

E5 = 5 and 2

E6 = 6 and 1

Pr(E1) = 1/7*1/7

= 1/49

Pr(E2) = 1/7*1/7

= 1/49

Pr(E3) = 1/7*1/7

= 1/49

Pr(E4) = 2/7*2/7

= 4/49

Pr(E5) = 1/7*1/7

= 1/49

Pr(E6)= 1/7*1/7

= 1/49

P(E) = Pr(E1) + Pr(E2) + Pr(E3) + Pr(E4) + Pr(E5) + Pr(E6)

= 1/49 + 1/49 + 1/49 + 4/49 + 1/49 + 1/49

= 9/49

When rolling loaded dice with particular probabilities of obtaining 3 and 4, the probability of obtaining a sum of 7 when two dice are rolled is 8/49.

Your question pertains to the concept of probability in mathematics, particularly when dealing with loaded dice and the probabilities of certain outcomes. In your scenario, you want to determine the probability of obtaining a sum of 7 given particular probabilities of rolling a 4 on the first die and a 3 on the second die.

In general, obtaining a sum of 7 is possible with the following combinations: 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, 6 and 1. With your loaded dice, however, only the combinations 4 and 3 and 3 and 4 are relevant. Given that the probability of rolling a 4 on the first die is 2/7, and the probability of rolling a 3 on the second die is also 2/7, the probability of rolling a 7 is (2/7)*(2/7)=4/49. As you are considering both the combinations 4 and 3, and 3 and 4, you need to multiply this result by 2 which gives a final probability of 8/49.

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Answer:

c. Stdev

Step-by-step explanation:

Excel stdev function is not appropriate to construct confidence interval estimate, because the estimation of the proportion of defective items that are produced by a certain machine has binomial distribution.

stdev fuction is used for calculating standard deviations where sample has more than two different values. (multinomial)

Norm.s.inv function calculates inverse of the standard normal cumulative distribution, and countif counts the number of cells that meet a criterion. Both functions are used to construct confidence interval estimate

Answer:

Step-by-step explanation:

Factor the given function:

        (x + 2)(x + 5)

f(x) = --------------------

         (x + 5)(x + 4)

The factor (x + 5) can be crossed out in numerator and denominator.  There is a 'hole' at x = -5 (which comes from setting (x + 5) = 0 and solving for x).

If we do cancel the (x + 5) factors, we are left with

           (x + 2)

f(x) =  ------------- .  We can't just substitute x = -5 because the original

           (x + 4)         function is not defined for that x value.  However, we

can locate the hole by letting x have the value of a litle more than -5, obtaining:

           ( -5+ + 2)

f(-5+) =  -------------, which comes out to approx. -3/-1, or +3 .  

            (-5+ + 4)    

So the hole location is (-5, 3).

f(x) = --------------------

         (x + 5)(x + 4)

The options are not clear but we can describe exponential function as follows

Exponential  function are of the form

[tex]y = b^x \; where\; b >0 = Exponentially\; Growing\\b<0 \; Exponentially\; Decaying \\\\x = Exponent[/tex]

The exponential functions are curved upwards gradually (figure attached )

Figure  1 (graph attached ) Shows the graph of function

[tex]y = 2^x[/tex]

We can   conclude that exponential function is a monotonous function and

depending upon the value of b the exponential function is either continuously increasing or continuously decreasing

[tex]y = -3^x[/tex]

as shown by Figure 2 (figure attached )

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Answer:

It's D

Hopefully this helps someone :D

Answer:

  4.47 years

Step-by-step explanation:

Fill in the numbers and solve for t.

  P = a·b^t

  15390 = 19000·0.954^t

  15390/19000 = 0.954^t . . . . . divide by 19000

  0.81 = 0.954^t . . . . . . . . . . . . . simplify

  log(0.81) = t·log(0.954) . . . . . . take the log

  t = log(0.81)/log(0.954) . . . . . . divide by the coefficient of t

  t ≈ 4.47

It will take about 4.47 years for the population to drop to 15390 organisms.

_____

A graphing calculator can be another way to solve a problem like this.

Answer:

download photomath

Step-by-step explanation:

I swear it would help you because it always help me.. just look carefully

Answer: x = 1,

y = 5

z = 2

Step-by-step explanation:

Answer:

[tex]cos^{-1} (\frac{8}{[tex]\sqrt{113}[/tex]} )[/tex]

Step-by-step explanation:

Given two vectors a and b,we are rquired to find the angle between them.

a=(8,7);b=(7,0).

Angle between two vectors can be found by dot product of them.

If a and b are two vectors then the dot product of them is given by|a||b|cos(α).

Where α is the angle between the vectors a and b.

Now [tex]|a|=\sqrt{113}\text{ } and\text{ } |b|=\sqrt{49}[/tex]. and [tex]a.b=8\ times 7+7\times 0[/tex] =56.

Now cosα=[tex]\frac{8}{\sqrt{113} }[/tex] so α= cosine inverse of that.

∴α=

[tex]cos^{-1} (\frac{8}{[tex]\sqrt{113}[/tex]} )[/tex]

Answer:

A youre welcome

Step-by-step explanation:

Answer:

t≅13.33h

Step-by-step explanation:

Adam (A) works at constant rate of 50tiles/h

Briana (B) works at constant rate of 55tiles/h, this means that A=50 tiles per hour and B=55 tiles per hour, then A+B = 105tiles/h together, but the floor consists of 1400tiles, so if 105 tiles are installed in one hour, then 1400 tiles in how long they will be installed?

t = 1400tiles*h/105tiles≅ 13.33 h

Answer:

  • 80%

Step-by-step explanation:

Consult your course reference materials.

Advice found on the Internet varies from 70% to 90%, depending on a number of factors. 70% has been a guide historically, but more recent advice favors higher numbers, it seems.

Answer:

[tex]x^2 + x - 72 = 0[/tex]

Explanation:

We are given product of two consecutive odd integers is equal to 72.

Let one integer be x , then since these are consecutive and odd so the other integer will be equal to x + 1.  

Their product is equal to 72. So,

x * (x + 1) = 72

=> [tex]x^2 + x = 72[/tex]

=>  [tex]x^2 + x - 72 = 0[/tex] is the required quadratic equation.

For this case we must find the solution of the following quadratic equation:

[tex]x ^ 2 + 5x + 7 = 0[/tex]

Where:

[tex]a = 1\\b = 5\\c = 7[/tex]

Then, the solution is given by:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]

Substituting the values:

[tex]x = \frac {-5 \pm \sqrt {5 ^ 2-4 (1) (7)}} {2 (1)}\\x = \frac {-5 \pm \sqrt {25-28}} {2}\\x = \frac {-5 \pm \sqrt {-3}} {2}[/tex]

By definition we have:[tex]i ^ 2 = -1[/tex]

[tex]x = \frac {-5 \pm \sqrt {3i ^ 2}} {2}\\x = \frac {-5 \pm i \sqrt {3}} {2}[/tex]

Thus, we have two complex roots.

Answer:

The equation has no real roots.

Answer:

Value of x is 20 and y is 120.

Step-by-step explanation:

Given,

m∠A = 70°, m∠B = 60°, m∠C = 50°,m∠D = (3x + 10)°, m∠E= (1/3y + 20)°, and m∠F = (z² + 14)°

Also,

ΔABC ≅ ΔDEF,

Since, the corresponding parts of congruent triangles are always congruent or equal.

⇒ m∠A = m∠D, m∠B = m∠E and m∠C = m∠F

When m∠A = m∠D

[tex]\implies 70 = 3x + 10[/tex]

[tex]70 - 10 = 3x[/tex]

[tex]60 = 3x[/tex]

[tex]\implies x =\frac{60}{3}=20[/tex]

When, m∠B = m∠E,

[tex]\implies 60 = \frac{1}{3}y + 20[/tex]

[tex]60 - 20 =\frac{1}{3}y[/tex]

[tex]40 =\frac{1}{3}y[/tex]

[tex]\implies y =3\times 40=120[/tex]

Answer:

11.57 units east, 13.79 units upwards

11.57i + 13.79j

Step-by-step explanation:

V = 18 units at an angle of 50° to the positive x-axis

In component Form, this is how each component is calculated

a = 18cos50° = 11.57 units east

b = 18sin50° = 13.79 units upwards

check if your answer is correct

[tex]\sqrt{11.57^{2} +13.79^{2} } = 18.0[/tex]

In vector component form ai + bj = 11.57i + 13.79j