Find the y -intercept and the slope of the line.
Write your answers in simplest form

5x - 2y = 2

Answer: [tex]y=\dfrac{1}{3}x+4[/tex]

Step-by-step explanation:

The equation of a line passing through (a,b) and (c,d) is given by :_

[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]

The given points :  (3,5) and (9,6)

Then , the equation of a line passing through (3,5) and (9,6)  will be :-

[tex]y-5=\dfrac{6-5}{9-3}(x-3)\\\\\Rightarrow\ y-5=\dfrac{1}{3}(x-3)\\\\\ y=\dfrac{1}{3}x-1+5\\\\\Rightarrow\ y=\dfrac{1}{3}x+4[/tex]

Hence, the equation of the line in slope -intercept form :  [tex]y=\dfrac{1}{3}x+4[/tex]

Final answer:

The answer provides the equation of the line passing through the points (3,5) and (9,6) in slope-intercept form.Using the points (3,5) and (9,6), the change in [tex]\( y \) is \( 6 - 5 = 1 \) and the change in \( x \) is \( 9 - 3 = 6 \). So, the slope is \( \frac{1}{6} \).[/tex]

Explanation:

Equation of the line:

The slope of a line represents the rate of change between two points on the line. It indicates how much the dependent variable (y-coordinate) changes for a given change in the independent variable (x-coordinate).

In this case, given the two points (3,5) and (9,6), we can calculate the slope using the formula:

[tex]\[ \text{slope} = \frac{{\text{change in } y}}{{\text{change in } x}} \][/tex]

Using the points (3,5) and (9,6), the change in [tex]\( y \) is \( 6 - 5 = 1 \) and the change in \( x \) is \( 9 - 3 = 6 \). So, the slope is \( \frac{1}{6} \).[/tex]

Answer:

Step-by-step explanation:

S.NO    QUATERS       PRICE ($)                 PRICE RELATIVES

                                                           [tex]I = \frac{q_i}{q_4} *100[/tex]

1                 q_1               10450                           104.51

2                q_2               10800                           108.01

3                 q_3               11450                            114.51

4                 q_2                9999                           100.00

Price Index is given as [tex]= \frac{\sum I}{n}[/tex]

                            [tex] = \frac{104.51+108.01+114.51+100}{4}[/tex]

                                       = 106.75

b) percentage point rise

[tex]for q_1 = \frac{q_2 -q_1}{q_1}*100[/tex]

          [tex]= \frac{108.01-104.51}{104.51}[/tex]

          = 3.34%

[tex]for q_2 = \frac{q_3 -q_2}{q_2}[/tex]

      [tex]= \frac{114.51-108.01}{108.01} *100[/tex]

          = 6.01%

[tex]for q_3 = \frac{q_4 -q_3}{q_3}[/tex]

         [tex]= \frac{100-114.51}{114.51} *100[/tex]

          = 12.67%

The bacterial population's growth is represented by the exponential growth function n(t) = 400 * 3^t, where 400 is the initial number of bacteria and t is the time in hours. After 3.5 hours, the population is estimated to be approximately 21236 bacteria.

The population of the bacteria can be modeled by an exponential growth function, specifically by considering its constant rate of tripling every hour. If we denote No as the initial number of bacteria, which is 400, and t as the time in hours, the number of bacteria n after time t would be represented by the function n(t) = No * 3^t. In this case, n(t) = 400 * 3^t.

Now, to estimate the rate of growth of the bacteria population after 3.5 hours, we substitute t = 3.5 into the equation which gives n(3.5) = 400 * 3^3.5. Calculating this to the nearest whole number gives approximately 21236, which represents the size of the bacteria population after 3.5 hours. This indicates a significant increase, a characteristic of exponential growth commonly observed in prokaryotes like bacteria under suitable conditions.

https://brainly.com/question/12490064

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To find an expression for the number of bacteria after t hours, we can use the following formula:

n(t) = 400 * [tex]3^{t}[/tex]

Now, let’s estimate the rate of growth after 3.5 hours:

n(3.5) = 400 * [tex]3^{3.5}[/tex]

Calculating this:

n(3.5) ≈ 400 × [tex]3^{3.5}[/tex]  ≈ 400 × 46.8 ≈  18,706.15

Rounded to the nearest whole number, the estimated population after 3.5 hours is 18,706 bacteria.

Answer:  p = 0.73

Step-by-step explanation:

Given that,

73% of the audience was under 20 years old :

so, probability (p) = 0.73

n = 146

Mean of the distribution of sample proportion = ?

According to central limit theorem,

np(1-p) ≥ 10

146 × 0.73(0.27) ≥ 10

28.77 ≥ 10

∴ Central limit theorem assumes that the sample distribution of the sample proportion is normally distributed.

Hence, the mean of the distribution of sample proportion:

μ = p = 0.73

[tex]\Sigma[/tex] should have parameterization

[tex]\vec r(\varphi,\theta)=a\sin\varphi\cos\theta\,\vec\imath+a\sin\varphi\sin\theta\,\vec\jmath+a\cos\varphi\,\vec k[/tex]

if it's supposed to capture the sphere of radius [tex]a[/tex] centered at the origin. ([tex]\sin\theta[/tex] is missing from the second component)

a. You should substitute [tex]x=a\sin\varphi\cos\theta[/tex] (missing [tex]\cos\theta[/tex] this time...). Then

[tex]x^2+y^2+z^2=(a\sin\varphi\cos\theta)^2+(a\sin\varphi\sin\theta)^2+(a\cos\varphi)^2[/tex]

[tex]x^2+y^2+z^2=a^2\left(\sin^2\varphi\cos^2\theta+\sin^2\varphi\sin^2\theta+\cos^2\varphi\right)[/tex]

[tex]x^2+y^2+z^2=a^2\left(\sin^2\varphi\left(\cos^2\theta+\sin^2\theta\right)+\cos^2\varphi\right)[/tex]

[tex]x^2+y^2+z^2=a^2\left(\sin^2\varphi+\cos^2\varphi\right)[/tex]

[tex]x^2+y^2+z^2=a^2[/tex]

as required.

b. We have

[tex]\vec r_\varphi=a\cos\varphi\cos\theta\,\vec\imath+a\cos\varphi\sin\theta\,\vec\jmath-a\sin\varphi\,\vec k[/tex]

[tex]\vec r_\theta=-a\sin\varphi\sin\theta\,\vec\imath+a\sin\varphi\cos\theta\,\vec\jmath[/tex]

[tex]\vec r_\varphi\times\vec r_\theta=a^2\sin^2\varphi\cos\theta\,\vec\imath+a^2\sin^2\varphi\sin\theta\,\vec\jmath+a^2\cos\varphi\sin\varphi\,\vec k[/tex]

[tex]\|\vec r_\varphi\times\vec r_\theta\|=a^2\sin\varphi[/tex]

c. The surface area of [tex]\Sigma[/tex] is

[tex]\displaystyle\iint_\Sigma\mathrm dS=a^2\int_0^\pi\int_0^{2\pi}\sin\varphi\,\mathrm d\theta\,\mathrm d\varphi[/tex]

You don't need a substitution to compute this. The integration limits are constant, so you can separate the variables to get two integrals. You'd end up with

[tex]\displaystyle\iint_\Sigma\mathrm dS=4\pi a^2[/tex]

# # #

Looks like there's an altogether different question being asked now. Parameterize [tex]\Sigma[/tex] by

[tex]\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath+u^2\,\vec k[/tex]

with [tex]\sqrt2\le u\le\sqrt6[/tex] and [tex]0\le v\le2\pi[/tex]. Then

[tex]\|\vec s_u\times\vec s_v\|=u\sqrt{1+4u^2}[/tex]

The surface area of [tex]\Sigma[/tex] is

[tex]\displaystyle\iint_\Sigma\mathrm dS=\int_0^{2\pi}\int_{\sqrt2}^{\sqrt6}u\sqrt{1+4u^2}\,\mathrm du\,\mathrm dv[/tex]

The integrand doesn't depend on [tex]v[/tex], so integration with respect to [tex]v[/tex] contributes a factor of [tex]2\pi[/tex]. Substitute [tex]w=1+4u^2[/tex] to get [tex]\mathrm dw=8u\,\mathrm du[/tex]. Then

[tex]\displaystyle\iint_\Sigma\mathrm dS=\frac\pi4\int_9^{25}\sqrt w\,\mathrm dw=\frac{49\pi}3[/tex]

# # #

Looks like yet another different question. No figure was included in your post, so I'll assume the normal vector points outward from the surface, away from the origin.

Parameterize [tex]\Sigma[/tex] by

[tex]\vec t(u,v)=u\,\vec\imath+u^2\,\vec\jmath+v\,\vec k[/tex]

with [tex]-1\le u\le1[/tex] and [tex]0\le v\le 2[/tex]. Take the normal vector to [tex]\Sigma[/tex] to be

[tex]\vec t_u\times\vec t_v=2u\,\vec\imath-\vec\jmath[/tex]

Then the flux of [tex]\vec F[/tex] across [tex]\Sigma[/tex] is

[tex]\displaystyle\iint_\Sigma\vec F\cdot\mathrm d\vec S=\int_0^2\int_{-1}^1(u^2\,\vec\jmath-uv\,\vec k)\cdot(2u\,\vec\imath-\vec\jmath)\,\mathrm du\,\mathrm dv[/tex]

[tex]\displaystyle\iint_\Sigma\vec F\cdot\mathrm d\vec S=-\int_0^2\int_{-1}^1u^2\,\mathrm du\,\mathrm dv[/tex]

[tex]\displaystyle\iint_\Sigma\vec F\cdot\mathrm d\vec S=-2\int_{-1}^1u^2\,\mathrm du=-\frac43[/tex]

If instead the direction is toward the origin, the flux would be positive.

Answer:

  DB = 13 cm

Step-by-step explanation:

ΔCAB ≅ ΔDBA by ASA, so CA ≅ DB by CPCTC.

CA = 13 cm, so DB = 13 cm.

Answer:

Step-by-step explanation:

Given : m(∠DAB) = m(∠CBA)

            m (CAB) = m(∠DBA)

            and CA = 13 cm

To find : measure of DB

In ΔCAB and ΔDAB

m(∠DAB) = m(∠CBA)     [given]

m(∠CAB) = m(∠DBA)     [given]

and AD is common in both the triangles.

Therefore, ΔCAB and ΔDAB will be congruent.    [By ASA property]

Therefore, CA = DB = 13 cm.

Answer:

(a, b) see the input matrices in the calculator image below

(c) see the output matrix in the calculator image below

Laura should use Supermarket II.

Step-by-step explanation:

(a) Your data is not clearly identified, so we have assumed that the item costs are listed for one supermarket before they are listed for the next. Then your matrix A will be ...

[tex]A=\left[\begin{array}{cccc}3.15&3.79&2.99&3.49\\2.99&2.89&2.79&3.29\\3.74&2.98&2.89&2.99\end{array}\right][/tex]

__

(b) The column matrix of purchase amounts will be ...

[tex]B=\left[\begin{array}{c}2&3&2&3\end{array}\right][/tex]

__

(c) It is somewhat tedious to do matrix multiplication by hand, so we have let a calculator do it. Some calculators offer easier data entry than others, and some insist that data be entered into tables before any calculation can be done. We have chosen this one (attached), not because its use is easiest, but because we can post a picture of the entry and the result.

[tex]C=\left[\begin{array}{c}34.12&30.10&31.17\end{array}\right][/tex]

Laura's total bill is least at Supermarket II.

_____

As you know, the row-column result of matrix multiplication is the element-by-element product of the 'row' of the left matrix by the 'column' of the right matrix. Here, that means the 2nd row 1st column of the output is computed from the 2nd row of A and the 1st (only) column of B:

  2.99·2 +2.89·3 +2.79·2 +3.29·3 = 5.98 +8.67 +5.58 +9.87

  = 30.10

Answer:

Skewed to the Right

Step-by-step explanation:

Hello, great question. These types are questions are the beginning steps for learning more advanced problems.

Since the mean household income is  $64,424 and the median was $50,303 then the mean is larger than the median. When this occurs then the constructed histogram is always Skewed to the Right. This is because there are a couple of really large values that affect the mean but not the middle value of the data set.

This in term leads to the graph dipping in values the farther right you go and increasing the farther left you go, as shown in the example picture below.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Answer:

x-intercept: (6,0)

y-intercept:  (0,4)

Step-by-step explanation:

The x-intercepts lay on the x-axis and therefore their y-coordinate is 0.

To find the x-intercept, you set y to 0 and solve for x.

2x+3y=12

Set y=0.

2x+3(0)=12

2x+0    =12

2x         =12

Divide both sides by 2:

 x          =12/2

 x          =6

The x-intercept is (x,y)=(6,0).

The y-intercepts lay on the y-axis and therefore their x-coordinate is 0.

To find the y-intercept, you set x to 0 solve for y.

2x+3y=12

2(0)+3y=12

0+3y    =12

3y         =12

Divide both sides by 3:

 y          =12/3

 y           =4

The y-intercept is (0,4).

The x-intercept of the equation 2x + 3y = 12 is (6,0) and y-intercept is (0,4).

To find the x-intercept of the equation 2x + 3y = 12, we set y to 0 and solve for x:

2x + 3(0) = 12
2x = 12
x = 6

So, the x-intercept is (6,0).

To find the y-intercept, we set x to 0 and solve for y:

2(0) + 3y = 12
3y = 12
y = 4

The y-intercept is (0,4).

Answer:

  (x, y, z) = (-4, 29, 17)

Step-by-step explanation:

These three equations have a unique solution. If you want "z arbitrary", you need to write a system of two equations with three variables (or, equivalently, a set of dependent equations).

It is convenient to let a graphing calculator, scientific calculator, or web site solve these.

_____

You can reduce the system to two equations in y and z by ...

  subtracting the last equation from the first:

     3y -7z = -32

  subtracting twice the last equation from the second:

     3y -2z = 53

Subtracting the first of these from the second, you get ...

  5z = 85

  z = 17

The remaining variable values fall out:

  y = (53+2z)/3 = 87/3 = 29

  x = -9 +2z -y = -9 +2(17) -29 = -4

These equations have the solution (x, y, z) = (-4, 29, 17).

We're looking for a solution of the form

[tex]y=\displaystyle\sum_{n=0}^\infty a_nx^n=a_0+a_1x+a_2x^2+\cdots[/tex]

Given that [tex]y(0)=1[/tex], we would end up with [tex]a_0=1[/tex].

Its first derivative is

[tex]y'=\displaystyle\sum_{n=0}^\infty na_nx^{n-1}=\sum_{n=1}^\infty na_nx^{n-1}=\sum_{n=0}^\infty(n+1)a_{n+1}x^n[/tex]

The shifting of the index here is useful in the next step. Substituting these series into the ODE gives

[tex]\displaystyle\sum_{n=0}^\infty(n+1)a_{n+1}x^n-\sum_{n=0}^\infty a_nx^n=x[/tex]

Both series start with the same-degree term [tex]x^0[/tex], so we can condense the left side into one series.

[tex]\displaystyle\sum_{n=0}^\infty\bigg((n+1)a_{n+1}-a_n\bigg)x^n=x[/tex]

Pull out the first two terms ([tex]x^0[/tex] and [tex]x^1[/tex]) of the series:

[tex]a_1-a_0+(2a_2-a_1)x+\displaystyle\sum_{n=2}^\infty\bigg((n+1)a_{n+1}-a_n\bigg)x^n=x[/tex]

Matching the coefficients of the [tex]x^0[/tex] and [tex]x^1[/tex] terms on either side tells us that

[tex]\begin{cases}a_1-a_0=0\\2a_2-a_1=1\end{cases}[/tex]

We know that [tex]a_0=1[/tex], so [tex]a_1=1[/tex] and [tex]a_2=1[/tex]. The rest of the coefficients, for [tex]n\ge2[/tex], are given according to the recurrence,

[tex](n+1)a_{n+1}-a_n=0\implies a_{n+1}=\dfrac{a_n}{n+1}[/tex]

so that [tex]a_3=\dfrac{a_2}3=\dfrac13[/tex], [tex]a_4=\dfrac{a_3}4=\dfrac1{12}[/tex], and [tex]a_5=\dfrac{a_4}5=\dfrac1{60}[/tex]. So the 5th degree approximation to the solution to this ODE centered at [tex]x=0[/tex] is

[tex]y\approx1+x+x^2+\dfrac{x^3}3+\dfrac{x^4}{12}+\dfrac{x^5}{60}[/tex]

Step-by-step explanation:

i think the answer is 42 to be exacr

Answer:

11.

Step-by-step explanation:

N = Nadia.

P = Pete.

S = postcards that Nadia gives to Pete.

N = 20 + P

P + S = 2+N-S

To calculate S, we replaces N of the first equation in the second equation:

P + S = 2 + 20 + P-S

2S = 2 + 20 + P - P

2S = 22

S = 22/2 = 11.

Answer:

d) criterion-based sample

Step-by-step explanation:

Quantitative research analyzes a given data and forms conclusions based on the analytical tools implemented in them. The most commonly used method to gather data is through questionnaires. Now, the generation of the questionnaires is important as the hypothesis you propose must be reflected after analysis of the data i.e., the criterion for each question must be selected carefully.

Answer: A) random sample

Explanation:

Random sample is the best sampling technique for the quantitative research as, random sample comes under the probability sampling and it occurred randomization when the parameters of the sampling frame has the equal opportunity for sampling. When we want to draw the random sample, the research started with the list of elements and members and this list sometimes contain the sampling frame.

Answer:

Probability from Urban Area = [tex]\frac{55}{89}[/tex]

Probability NOT from Rural Area = [tex]\frac{83}{89}[/tex]

Step-by-step explanation:

Total 178

Urban 110

Suburban 56

Rural 12

Hence, probability of x is number of x divided by total.

So, probability that she is from an urban area = 110/178 = 55/89

And

probability NOT a rural area (means urban and suburban which is 110+56=166) = 166/178 = 83/89

To calculate the probability of selecting a participant from an urban area, divide the number of urban participants (110) by the total number of participants (178), yielding approximately 0.61798. For the probability of not a rural area, sum the urban and suburban participants (110 + 56) and divide by the total, which gives approximately 0.93258.

The question asks about finding the probability of a participant being from an urban area and not from a rural area in a sample of young women in a STEM program.

The total number of participants is 178. Of these, 110 are from urban areas. To find the probability of selecting a participant from an urban area, we divide the number of urban participants by the total number of participants:

Probability (Urban) = Number of Urban Participants / Total Number of Participants = 110 / 178 ≈ 0.61798

Similarly, to find the probability of not selecting a participant from a rural area, we need to first find the number of participants who are not from rural areas. This is the sum of urban and suburban participants, or 110 + 56. Then we calculate:

Probability (Not Rural) = Number of Non-Rural Participants / Total Number of Participants = (110 + 56) / 178 ≈ 0.93258

We know that the binomial theorem for finding the probability of x success out of a total of n experiments is given  by:

[tex]b(x;n;p)=n_C_x\cdot p^x\cdot (1-p)^{n-x}[/tex]

(a)

b(5; 8, 0.25)

is given by:

[tex]8_C_5\cdot (0.25)^5\cdot (1-0.25)^{8-5}\\\\=8_C_5\cdot (0.25)^5\cdot (0.75)^3\\\\=56\cdot (0.25)^5\cdot (0.75)^3\\\\=0.023[/tex]

                    Hence, the answer is:  0.023

(b)

b(6; 8, 0.65)

i.e. it is calculated by:

[tex]=8_C_6\cdot (0.65)^6\cdot (1-0.65)^{8-6}\\\\=8_C_6\cdot (0.65)^6\cdot (0.35)^2\\\\=0.259[/tex]

              Hence, the answer is: 0.259

(c)

P(3 ≤ X ≤ 5) when n = 7 and p = 0.55

[tex]P(3\leq x\leq 5)=P(X=3)+P(X=4)+P(X=5)[/tex]

Now,

[tex]P(X=3)=7_C_3\cdot (0.55)^3\cdot (1-0.55)^{7-3}\\\\P(X=3)=7_C_3\cdot (0.55)^3\cdot (0.45)^{4}\\\\P(X=3)=0.239[/tex]

[tex]P(X=4)=7_C_4\cdot (0.55)^4\cdot (1-0.55)^{7-4}\\\\P(X=4)=7_C_4\cdot (0.55)^4\cdot (0.45)^{3}\\\\P(X=4)=0.292[/tex]

[tex]P(X=5)=7_C_5\cdot (0.55)^5\cdot (1-0.55)^{7-5}\\\\P(X=3)=7_C_5\cdot (0.55)^5\cdot (0.45)^{2}\\\\P(X=3)=0.214[/tex]

                                    Hence,

                  [tex]P(3\leq x\leq 5)=0.745[/tex]

(d)

P(1 ≤ X) when n = 9 and p = 0.1 .613

[tex]P(1\leq X)=1-P(X=0)[/tex]

Also,

[tex]P(X=0)=9_C_0\cdot (0.1)^{0}\cdot (1-0.1)^{9-0}\\\\i.e.\\\\P(X=0)=1\cdot 1\cdot (0.9)^9\\\\P(X=0)=0.387[/tex]

i.e.

[tex]P(1\leq X)=1-0.387[/tex]

                     Hence, we get:

                  [tex]P(1\leq X)=0.613[/tex]

To compute binomial probabilities using the formula b(x; n, p), you can substitute the values of x, n, and p into the formula and solve for the probability. For example, b(5; 8, 0.25) represents the probability of getting exactly 5 successes in 8 trials with a success probability of 0.25. (a) b(5; 8, 0.25) = 0.023. (b) b(6; 8, 0.65) = 0.259. (c) P(3 ≤ X ≤ 5) when n = 7 and p = 0.55 is approximately 0.745. (d) P(1 ≤ X) when n = 9 and p = 0.1 is approximately 0.613.

Binomial probabilities can be calculated using the formula for b(x; n, p). For example, to calculate b(5; 8, 0.25), you can use the formula:

[tex]b(5; 8, 0.25) = C(8, 5) * (0.25)^5 * (0.75)^3[/tex]

where C(8, 5) represents the number of combinations of 8 items taken 5 at a time. Solving this equation will give you the probability of getting exactly 5 successes in 8 trials with a success probability of 0.25.

Similarly, for b(6; 8, 0.65), you can use the formula:

[tex]b(6; 8, 0.65) = C(8, 6) * (0.65)^6 * (0.35)^2[/tex]

where C(8, 6) represents the number of combinations of 8 items taken 6 at a time. Solving this equation will give you the probability of getting exactly 6 successes in 8 trials with a success probability of 0.65.

(c) To calculate the probability of 3 ≤ X ≤ 5 when n = 7 and p = 0.55, you need to calculate the probabilities of 3, 4, and 5 successes individually and then sum them up.

(d) To calculate P(1 ≤ X) when n = 9 and p = 0.1, you need to calculate the probabilities of 1, 2, 3, ..., 9 successes individually and then sum them up.

Answer:

Step-by-step explanation:

Mean = 14

Std deviation of sample s = 0.64

n = sample size =7

Std error = [tex]\frac{s}{\sqrt{n} } =0.2419[/tex]

t critical for 95% two tailed = 2.02

Margin of error = 2.02*SE = 0.4886

a)Conf interval lower bound = 14-0.4886 = 13.5114

b)Upper bound = 14+0.4886 = 14.4886

c)Assumption

the data need to follow a normal distribution

Answer:

monthly payment=$322.52

Step-by-step explanation:

cost of house=$290,000

down payment= 20%

interest  monthly = 4.2%

interest rate compounded monthly so (i)=4.2/12=0.35%

months= [tex]30\times 12[/tex]=360 months

down payment = [tex]0.2\times 290000[/tex]

                         =$58000

amount to be paid(P)=$232,000

[tex]P=R\frac{(1+r)^n-1}{i}\\232000=R\frac{(1+0.0035)^{360}-1}{0.0035}\\232000=R\times 719.33[/tex]

R=$322.52

sara's monthly payment will be $322.52

Answer:

Option 2: m∠1 = 147°, m∠2 = 80°, m∠3 = 148°

Step-by-step explanation:

Step 1: Consider triangle ABC from the picture attached below.

Lets find angle x

x + 47 + 33 = 180 (because all angles of a triangle are equal to 180°)

x = 100°

Angle x = Angle y = 100° (because vertically opposite angles are equal)

Step 2: Find angle 2

Angle 2 = 180 - angle x (because angle on a straight line is 180°)

Angle 2 = 180 - 100

Angle 2 = 80°

Step 3: Find angle z

48 + y + z = 180° (because all angles of a triangle are equal to 180°)

z = 32°

Angle 3 = 180 - angle z (because angle on a straight line is 180°)

Angle 3 = 180 - 32

Angle 3 = 148°

Step 4: Find angle 1

Angle 1 = 180 - 33 (because angle on a straight line is 180°)

Angle 1 = 147°

Therefore m∠1 = 147°, m∠2 = 80°, m∠3 = 148°

Option 2 is correct

!!

The slope of the tangent line to the curve defined by x = 6 + ln(t), y = t^2 + 6 at the point (6,7) can be found by differentiating x and y with respect to t and then substituting t = 1. The equation of the tangent line is y = 2x -5.

To find the equation of the tangent to the curve at the given point, we will first need to find the derivative (slope) at the given point. The equations given are x = 6 + ln(t) and y = t2 + 6. Given point is (6, 7).

Without eliminating the parameter, we differentiate both x and y with respect to t. This allows us to find dx/dt = 1/t and dy/dt = 2t. The slope of the tangent line at (6, 7) is then (dy/dt) / (dx/dt) = 2t * t = 2*t2.

Substitute the given point (6,7) into x = 6 + ln(t), to obtain t = e0 = 1. Therefore, the slope of the tangent line is 2*12 = 2.

The equation of the tangent line can be written as: (y - y1) = m*(x - x1), where m = 2 is the slope, and (x1, y1) is the given point (6, 7).Substitute these into the equation, gets us: y-7 = 2*(x - 6), which can be simplified to: y = 2x -5.

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The equation of the tangent to the curve at the point (6, 7) is y = 2x - 5.

To find the equation of the tangent to the curve without eliminating the parameter, we can use the parametric equations: x = 6 + ln(t) and y = t^2 + 6.

First, we need to find the derivative of y with respect to x and evaluate it at the given point (6, 7).

The derivative of y with respect to x is dy/dx = (dy/dt)/(dx/dt).

From the given equations, we can calculate dx/dt = 1/t and dy/dt = 2t.

Substituting these values into the derivative expression, we have dy/dx = (2t)/(1/t) = 2t^2.

Now, substitute the given x-coordinate (6) into the equation for x to find the corresponding t-value: 6 = 6 + ln(t) => ln(t) = 0 => t = 1.

Now, substitute the t-value (1) into the equation for y to find the corresponding y-coordinate: y = 1^2 + 6 = 7.

Therefore, the slope of the tangent at the point (6, 7) is 2(1)^2 = 2.

Using the point-slope form of a line, we can write the equation of the tangent line: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the tangent.

Plugging in the values, we have y - 7 = 2(x - 6).

Simplifying the equation, we get y = 2x - 5.

Therefore, the equation of the tangent to the curve at the point (6, 7) is y = 2x - 5.

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Answer:

1/91

Step-by-step explanation:

SUMMER VACATION

There are 14 letters, 2 of them are A's

P (1st letter is an A) = 2/14=1/7

Then we keep the A

SUMMER VCATION

There are 13 letters, 1 of them is an A's

P (2nd letter is an A) = 1/13

P (1st A, 2nd A) = 1/7 * 1/13 = 1/91

Answer:

1/91

Step-by-step explanation:

Answer:

[tex]P=775[/tex]

Step-by-step explanation:

The Simple Interest Equation is [tex]A = P(1 + rt)[/tex]

where

A = Total Accrued Amount (principal + interest)

P = Principal Amount

I = Interest Amount

t = Time Period involved in months or years

In this case, we do not know the values ​​of the equation (A and P), but we know the amount of interest accrued

If we define our principal whit this formula, we are able to know the rest of the values:

[tex]A-P= interest[/tex]

clearing

[tex]A=interest+P[/tex]

replacing

[tex]426.25 + P = P (1+(0.11(5))[/tex]

Solving

[tex]426.25+P=1.55P[/tex]

[tex]P-1.55P=-426.25[/tex]

[tex]-0.55P=-426.65[/tex]

[tex]P=\frac{-426.25}{-0.55}[/tex]

[tex]P=775[/tex]

Answer:

so Lester receive money is $13762.5  

Step-by-step explanation:

Given data in question

principal = $15000

discount = 8* 1/4 % i.e. = 8.25% = 0.0825

to find out

Lester receive money ?

solution

we know ordinary interest formula i.e.

receive money = principal ( 1 - discount )  ...........1

we all value principal and discount in equation 1 and we get receive money

receive money = principal ( 1 - discount )

receive money = $15000 ( 1 - 0.0825)

receive money = $ 13762.5  

so Lester receive money is $13762.5  

Lester received a total of $14,417.50 as proceeds when he discounted the note at Brome Bank.

Lester accepted a $15,000, 7 3/4%, 180-day note from Ryan O'Flynn on July 18. On October 5, Lester discounted the note at Brome Bank at 8 1/4%.

To calculate the proceeds Lester received, we need to find the simple interest earned on the note for 180 days. First, find the interest earned:

Principal x Rate x Time = Interest

$15,000 x 7.75% x (180/360) = $582.50

Next, subtract the interest earned from the face value of the note to find the proceeds Lester received:

$15,000 - $582.50 = $14,417.50

Therefore, Lester received $14,417.50.

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Answer: 0.9932

Step-by-step explanation:

Given : Mean : [tex]\mu=\$2.837\text{ per gallon }[/tex]

Standard deviation : [tex]\sigma = \$0.009\text{ per gallon}[/tex]

a) The formula for z -score :

[tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

Sample size = 55

For x= $2.834​ ,

[tex]z=\dfrac{2.834-2.837}{\dfrac{0.009}{\sqrt{55}}}\approx2.47[/tex]

The p-value = [tex]P(z<2.47)=[/tex]

[tex]0.9932443\approx0.9932[/tex]

Thus, the probability that the mean price per gallon is less than ​$2.834 is approximately 0.9932 .

The question asks about finding the probability that the mean price per gallon of gas is less than $2.834. This is a statistics question and requires calculation of Z-score and the finite correction factor should be considered due to our sample size being more than 5% of the population.

The question asks about the probability of a certain mean price per gallon for a sub-sample drawn from a larger population. In statistics, we often use Z-scores to calculate the probability of a score occurring within a standard distribution, but the entire population parameters should be known. Hence, we should use the finite correction factor (a.k.a the population correction factor) due to our sample size being more than 5% of the population.

In this case, the Z-score is calculated as follows:

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Answer: 0.965

Step-by-step explanation:

Given : Water use in the summer is normally distributed with

[tex]\mu=311.4\text{ million gallons per day}[/tex]

[tex]\sigma=40 \text{ million gallons per day}[/tex]

Let X be the random variable that represents the quantity of water required on a particular day.

Z-score : [tex]\dfrac{x-\mu}{\sigma}[/tex]

[tex]\dfrac{350-311.4}{40}=0.965[/tex]

Now, the probability that a day requires more water than is stored in city reservoirs is given by:-

[tex]P(x>350)=P(z>0.965)=1-P(z<0.965)[/tex]

We can see that on comparing the above value to the given P(X > 350)= 1 - P(Z < b) , we get the value of b is 0.965.

Answer:

 The candle has a height of 21.4 cm after burning for 22 hours.

Step-by-step explanation:

let x=hours, m=rate of change,  and  y= candle height

First you have to find the slope or, rate of change using the slope formula.  y2-y1 divided by x2-x1   .        

Here is our points    (9,     17.5)   and   (24,    22)

                                    x1       y1                 x2     y2

Now we put these into the equation and solve

[tex]\frac{22-17.5}{24-9}[/tex]   =[tex]\frac{3}{10}[/tex]

Now that we have the slope of 3/10 we can use this to find the y-intercept using the point-slope equation.

[tex]y-y_{1} =m(x-x_{1} )[/tex]                 y-17.5= .3(x-9) Solve

y-17.5=.3x-2.7                                        y  -14.8=      .3x

 +2.7         +2.7                                         +14.8               +14.8

y=.3x+14.8                     the y-intercept is 14.8

Now we use this equation to  plug in the 22 hours.

y=.3(22) +14.8

y=6.6+14.8

y= 21.4    The candle has a height of 21.4 cm after burning for 22 hours.

Answer:

-28 is the answer.

Step-by-step explanation:

84-56=28

56+28=84

-56+-28=-84

Answer:

[tex] - 56 + x = - 84 \\ x = 56 - 84 \\ \boxed{ x = - 28}[/tex]

Answer: 8

Step-by-step explanation:

The formula to calculate the simple interest is given by :-

[tex]S.I. =Prt[/tex], where P is the principal amount , r is rate of interest and t is time.

Given: The principal amount : P = $225

The rate of interest : r = 3.5% =0.035

Simple Interest : SI = $63

Put these value in the above formula , we get

[tex] 63=225\times0.035t\\\\\Rightarrow\ t=\dfrac{63}{225\times0.035}\\\\\Rightarrow\ t=8[/tex]

Hence, the term of loan = 8

Answer:

A. [tex]\text{Set builder}=\{2x:x\in Z,x>0\}[/tex]

B. [tex]\text{Set builder}=\{2x-1:x\in Z,x>0\}[/tex]

Step-by-step explanation:

Set builder form is a form that defines the domain.

A.

The given arithmetic sequence is

2,4,6,8,10,.....

Here all terms are even numbers. The first term is 2 and the common difference is 2.

All the elements are multiple of 2. So, the elements are defined as 2x where x is a non zero positive integer.

The set of all 2x such that x is an integer greater than 0.

[tex]\text{Set builder}=\{2x:x\in Z,x>0\}[/tex]

Therefore the set builder form of given elements is [tex]\{2x:x\in Z,x>0\}[/tex].

B.

The given arithmetic sequence is

1,3,5,7,....

Here all terms are odd numbers. The first term is 1 and the common difference is 2.

All the elements are 1 less than twice of an integer. So, the elements are defined as 2x-1 where x is a non zero positive integer.

The set of all 2x-1 such that x is an integer greater than 0.

[tex]\text{Set builder}=\{2x-1:x\in Z,x>0\}[/tex]

Therefore the set builder form of given elements is [tex]\{2x-1:x\in Z,x>0\}[/tex].

Answer:

This is a binomial experiment

Step-by-step explanation:

Binomial experiment is an experiment in which for each trial there are only two outcomes.

In case of the given experiment, it is being asked either the applicants were admitted to the Park university or not, it has only two outcomes, Yes and no. So having only two options as outcomes this experiment is a binomial experiment ..