The formula A(t) = 756e^(0.035)t models the growth of an investment due to continuously compounded interest. What does 0.035 stand for?
A) the numbers of years since the initial investment
B) the amount after t years
C) the initial amount invested
D) the interest rate

Answer:

n=3.5, n=0

Step-by-step explanation:

Open the parenthesis

2n(-4n)-7(-4n)=0

-8n^2+28n=0

Factor:

n(-8n+28)=0

Solve:

n=0, or -8n+28=0

-8n=-28

8n=28

n=28/8

n=3.5

n can be either 3.5 or 0

Answer:

0, 7/2

Step-by-step explanation:

See image below:)

243 = the pages read on Saturday

243 - 53 = 190 = the pages read on Sunday

190 + 243 =  433 = total pages read

Answer = 433

Answer:

D

Step-by-step explanation:

From the given scatter plot, it is positive correlation.

Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.

Interpretation of correlation

From the given graph,

The coordinates points are in increasing order.

Therefore, the correlation is positive.

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Answer:

A) P ( chicken is small ) = 0.3085,  P ( chicken is medium ) = 0.6621

   P (chicken is large ) = 0.0294

B) C = 3.9233

C) 0.1404

Step-by-step explanation:

A) Probabilities

i) P ( chicken is small )

 P( w ≤ 3.5 ) = Fw ( 3 .5 )

                    = F ( 3.5 - 3.8 / 0.6 )

                    = F ( -0.5 ) = 1 - F( 0.5 ) [∵ F(-x) 1 - F(x) ]

                    = 1 - 0.6915 ( from Table )

                    = 0.3085

ii) P ( chicken is medium )

  P ( 3.5 < w < 4.9 )

  P ( w < 4.9 ) - P ( w < 3.5 )

= Fw ( 4.9 ) - Fw ( 3.5 )

= F ( 4.9 - 3.8 / 0.6 ) - 0.3085

= 0.9706 - 0.3085 = 0.6621  

iii) P (chicken is large )

= P ( w > 4.9 )

= 1 - P ( w < 4.9 )

= 1 - Fw ( 4.9 ) = 1 - 0.9706 = 0.0294

B) Find c

Given:  P( w < c ) = 0.6

Fw ( c ) = 0.6

F ( c - 3.8 / 0.6 ) = 0.6

c - 3.8 / 0.6 = 0.2055 ( from table )

∴C = 3.9233

C) P ( 3 out of 5 = small )

P ( 3 of 5 = small ) = 0.1404

attached below is a detailed solution

Step-by-step explanation:

We need to find a midpoint. A midpoint splits the two end coordinates to meet at a point.

Use midpoint formula

[tex] \frac{ - 2 + 10}{2} = 4[/tex]

[tex] \frac{ - 11 + 1}{2} = - 5[/tex]

So the coordinates will be at

(4,-5)

Answer:

x = (-1 ± √21) / 2

The first choice

Step-by-step explanation:

x² = 5 - x

Put in standard form

x² + x - 5 = 0

Use quadratic equation

x = ( -b ± √( b² - 4ac) ) / (2a)

Plug in a = 1, b = 1 , c = -5

x = (-1 ± √( 1² - 4*1*(-5)) ) / 2

evaluate

x = (-1 ± √21) / 2

Answer:

times up the outside bc we know the outside is the area

Answer:

Marmik = 800; Sujata = 600; Kapil = 400

Step-by-step explanation:

Given

Let

[tex]M \to Marmik[/tex]

[tex]S \to Sujata[/tex]

[tex]K \to Kapil[/tex]

Given

[tex]M:S:K = \frac{1}{3}:\frac{1}{4}:\frac{1}{6}[/tex]

[tex]Amount = 1800[/tex]

Required

Divide

We have:

[tex]M:S:K = \frac{1}{3}:\frac{1}{4}:\frac{1}{6}[/tex]

Multiply the ratio by 12 (to convert them to whole numbers)

[tex]M:S:K = 12 *\frac{1}{3}:12*\frac{1}{4}:12*\frac{1}{6}[/tex]

[tex]M:S:K = 4 : 3 : 2[/tex]

The total ratio is:

[tex]Total = 4 + 3 + 2 = 9[/tex]

So, the amount each collected is:

[tex]Marmik = \frac{M}{Total} * Amount[/tex]

[tex]Marmik = \frac{4}{9} *1800 = 800[/tex]

Using the same formula for others, we have:

[tex]Sujata = \frac{3}{9} *1800 = 600[/tex]

[tex]Kapil = \frac{2}{9} *1800 = 400[/tex]

Answer:

The answer seems to be 3/1.

Step-by-step explanation:

Use the equation:

(y2-y1)/(x2-x1)

Answer:

Slope = 15/4

Step-by-step explanation:

Use the slope formula and you'll get the same answer.

Hope this helps:)

Answer:

Option B. ( x=1,-5/2 Or x=-5/2,1)

Step-by-step explanation:

2x2+3x−5=0

Step 1: Factor left side of equation.

(2x+5)(x−1)=0

Step 2: Set factors equal to 0.

2x+5=0 or x−1=0

x=−5/2  or x=1  

(The Answer you can just switch it around but dont worry its still the same answer nothing change...)

9514 1404 393

Answer:

  a) ADC

  b) ABC

  c) ACB

  d) CAD, DAB

  e) CDm, BDA

  f) ABD

Step-by-step explanation:

a) Any of the letters on lines going through point D could be used to name an angle with DC as one side. (Letters s and C would name an angle of measure zero, so might not be of interest.)

  ∠ADC has side DC

__

b) Any angle name with B in the middle will have B as its vertex.

  ∠ABD is an angle with vertex B

__

c) Ray CE is coincident with ray CD, so ...

  ∠ACE is another name for ∠ACD

__

d) Adjacent angles share a side, typically between the two angles. A linear pair of angles will be adjacent angles.

  ∠BAD and ∠CAD are adjacent angles

__

e) In order to properly name a pair of vertical angles, we need to be able to name two sets of opposite rays that share end points. Opposite rays emanate from points C and D, but no named points are seen outboard of those intersections. If we use 'm' as the name of a point on line m, then we can say a pair of vertical angles is ...

  CDm and BDA are two vertically opposite angles

__

f) The supplement to EBD will be the other angle that makes a linear pair with angle EBD. It is defined using point A on the ray opposite ray BE.

  ∠ABD is the supplement of ∠EBD

Answer:

y=3x-2

Step-by-step explanation:

y = mx + b

m = slope

b=yint

y=3(slope)x+ -2(y int)

Using the Pythagorean theorem,

[tex]6^{2}+y^{2}=(3+9)^{2}\\\\36+y^2=144\\\\y^2=108\\\\y=\boxed{6\sqrt{3}}[/tex]

Answer:

The speed is 60 mph.

Step-by-step explanation:

distance = 42 miles

Let he drove with speed v and time is t.

distance = speed x time

42 = v t ..... (1)

42 = (v + 10)(t - 1/10) ..... (2)

[tex]42 = 42 -\frac{v}{10}+ 10 t - 1\\\\t =\frac{10+v}{100}\\\\Put in (1)\\\\42 = \frac{v(10+v)}{100}\\\\v^2 + 10 v - 4200 = 0 \\\\v = \frac{-10\pm \sqrt{100+4\times 4200}}{2}\\\\v =\frac{- 10 \pm 130}{2}\\\\v =- 70 mph, 60mph[/tex]

So, the speed cannot be negative so the speed is 60 mph.

Answer:

-30+10b=-22

32-22=10b

10b=10

-32+10=-22

hope it helps

Answer:

221

Step-by-step explanation:

5(3)2-4

Answer:

221

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\frac{-2}{3}*\frac{3}{5}+\frac{5}{2}-\frac{3}{5}*\frac{1}{6}=\frac{-2}{5}+\frac{5}{2}-\frac{1}{5*2}\\\\= \frac{-2}{5}+\frac{5}{2}-\frac{1}{10}\\\\=\frac{-2*2}{5*2}+\frac{5*5}{2*5}-\frac{1}{10}\\\\=\frac{-4}{10}+\frac{25}{10}-\frac{1}{10}\\\\=\frac{-4+25-1}{10}\\\\=\frac{20}{10}\\\\= 2[/tex]

Answer:

a) 0.3 liters

b) 3 ÷ 10 = 0.3 liters

Step-by-step explanation:

3 ÷ 10

3 × 1/10

0.3

The solution is:

The figure has 4 lines of symmetry.

- A vertical line through the middle of the figure.

- A horizontal line through the middle of the figure.

- The two diagonals through the figure are lines of symmetry too.

In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In 2D there is a line/axis of symmetry, in 3D a plane of symmetry.

here, we have,

Explanation

Lines of symmetry refer to lines that can be drawn on figures and the figure on either sides of the line will be mirror images of each other.

For example, for this figure given, if a vertical line is drawn straight through the middle of the figure, the two resulting figures on either sides of the vertical line will be mirror images of each other.

So, the other lines of symmetry for this include

- A horizontal line through the middle of the figure

- The two diagonals through the figure are lines of symmetry too.

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Answer:

a. Z = -1.175.

b. Z = 1.34.

c. |Z| = 2.054.

d. |Z| = 1.28.

Step-by-step explanation:

Z-score:

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.

a. The critical z-score for a left-tailed test at a 12% significance level

Left-tailed test: The region of interest is the 12th percentile or below.

Thus, the critical z-score is Z with a p-value of 0.12, so Z = -1.175.

b. The critical z-score for a right-tailed test at a 9% significance level

Right-tailed test: The region of interest is the 100 - 9 = 91th percentile and above.

Thus, the critical z-score is Z with a p-value of 0.91, so Z = 1.34.

c. The critical z-score for a two-sided test at a 4% significance level is 1.75.

Two-tailed test: The region of interest is between the 4/2 = 2th percentile and the 100 - (4/2) = 98th percentile.

Thus, the critical z-score is |Z| with a p-value of 0.02 or 0.98, so |Z| = 2.054.

d. The critical z-score for a two-sided test at a 20% significance level is 0.85.

Region of interest is between the 20/2 = 10th percentile and the 100 - (20/2) = 90th percentile.

Thus, the critical z-score is |Z| with a p-value of 0.1 or 0.9, so |Z| = 1.28.

Answer:

you see on the right where the ( - ) are put the dot at -3 which is on the line because y } -x (which means your on the negative side) + 3 is -6 so put the dot on 6

Answer:

118.8 cubic inches

Step-by-step explanation:

volume of a cone is

[tex]vol \: = \frac{1}{3} \times \pi \times \frac{ {d}^{2} }{4} \times h[/tex]

where d is base diameter and

h is cone height.

hence

[tex]vol \: = \frac{1}{3} \times \pi \times \frac{ {5.5}^{2} }{4} \times 15 \\ = \pi \times \frac{30.25}{4} \times 5 \\ = 118.8 \: cu \: in[/tex]

The volume of the cone-shaped mold is 118.73 in³

Volume is the measure of the capacity that an object holds. For example, if a cup can hold 100 ml of water up to the brim, its volume is said to be 100 ml.

Given that a cone shaped mold is filled with the cake batter, the height of the mold is 15 inches, and the base diameter is 5.5,

We need to find the volume of the mold,

Volume of the cone = π × radius² × height / 3

= 3.14 × 2.75² × 15 / 3

= 118.73

Hence, the volume of the cone-shaped mold is 118.73 in³

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Answer:

The quadratic function represented by the graph is [tex]y = x^{2}-6\cdot x + 8[/tex].

Step-by-step explanation:

Parabolae are defined by second order polynomials, that is, a polynomial of the form:

[tex]y = a\cdot x^{2} + b\cdot x + c[/tex] (1)

Where:

[tex]x[/tex] - Independent variable.

[tex]y[/tex] - Dependent variable.

[tex]a, b, c[/tex] - Coefficients.

By Algebra, we know can calculate the set of all coefficients based on the knowledge of three distinct points. According to the graph, we have the following points: [tex](x_{1}, y_{1}) = (2, 0)[/tex], [tex](x_{2}, y_{2}) = (4, 0)[/tex] and [tex](x_{3}, y_{3}) = (6, 8)[/tex], and the resulting system of linear equations is:

[tex]4\cdot a + 2\cdot b + c = 0[/tex] (2)

[tex]16\cdot a + 4\cdot b + c = 0[/tex] (3)

[tex]36\cdot a + 6\cdot b + c = 8[/tex] (4)

The solution of the system of linear equations is:

[tex]a = 1, b = -6, c = 8[/tex]

Hence, the quadratic function represented by the graph is [tex]y = x^{2}-6\cdot x + 8[/tex].

Answer:

y = 1/4x - 4

Step-by-step explanation:

The slope is four points behind the origin, so we subtract -4 from the equation:

y = 1/4x - 4

use two points on the line to find the slope:

(0,-4) (4,2)

Slope = change in y over change in x

Slope = (2 - -4) / (4-0) = 6/4 = 3/2

Y-intercept is the y value when x is 0, the line goes through y=2 at x = 0, so the t intercept is 2

The equation is:

Y = 3/2x + 2

Answer:

[tex]C = 29.53x[/tex]

Step-by-step explanation:

Given

[tex]Unit\ cost = \$29.53[/tex]

Required

The cost of fencing (C)

The cost is calculated as:

[tex]C = Unit\ Cost * Perimeter\ of fencing[/tex]

Let:

[tex]x \to Perimeter\ of fencing[/tex]

So, we have:

[tex]C = Unit\ Cost * x[/tex]

[tex]C = 29.53 * x[/tex]

[tex]C = 29.53x[/tex]

The question cannot be solved further since the dimension of the fence is not given

If you know the dimension, calculate the fence perimeter and substitute the value for x

Answer:

Area of the bookmark = 52.56 cm²

Step-by-step explanation:

The two semicircles attached at both end of the rectangle will give us a full circle.

Therefore,

Area of the bookmark = area of rectangle + Area of a circle

Area of the bookmark = L × W + πr²

Length (L) = 10 cm

Width (W) = 4 cm

radius (r) = ½(4) = 2 cm

π = 3.14

Plug in the values into the equation

Area of bookmark = 10 × 4 + 3.14 × 2²

= 40 + 12.56

= 52.56 cm²

9514 1404 393

Answer:

  8

Step-by-step explanation:

The number of servings can be found by dividing the quantity available by the amount per serving.

  (6 cups)/(3/4 cup/serving) = (6)(4/3) servings = 8 servings