The sign of the product of -35 and -625 is positive, negative, or zero
Answer:
Positive
Step-by-step explanation:
The product of two negative numbers has a positive sign, whereas the product of a positive and a negative number is negative.
Since -35 and -625 are both negative, they would have a positive sign for their product.
Hope this helps.
Answer: Positive
Step-by-step explanation:
Keith received a gift card of $90 for a pizza restaurant. The restaurant charges $15 per pizza. Mary received a gift card of $110 for a different pizza restaurant. The restaurant charges $20 per pizza.
Let x be the number of pizzas purchased. For each card, write an expression for the amount of money left on the card after purchasing x pizzas.
Amount of money left on Keith's card in dollars = __________
Amount of money left on Mary's card in dollars=____________
Write an equation to show that the two cards have the same amount of money left on them [don't know how to do this part.
Answer:
a)Amount of money left on Keith's card in dollars = $90 - $15x
= $(90 - 15)
b) Amount of money left on Mary's card in dollars= $110 - $20x
= $(110 - 20x)
c) Write an equation to show that the two cards have the same amount of money left on them [don't know how to do this part.
$90 - 15x = $110 - 20x
Step-by-step explanation:
Let x be the number of pizzas purchased. For each card, write an expression for the amount of money left on the card after purchasing x pizzas.
For Keith
Keith received a gift card of $90 for a pizza restaurant. The restaurant charges $15 per pizza.
x numbers of pizza costs = $15x
Hence, the amount of money left on Keith's card after purchasing x pizzas =
$90 - $15x
For Mary,
Mary received a gift card of $110 for a different pizza restaurant. The restaurant charges $20 per pizza.
Hence, x number of pizzas cost =$20 × x
= $20x
Therefore, the amount of money left on Mary's card after she buys x pizzas =
$110 - $20x
Amount of money left on Keith's card in dollars = __________
Amount of money left on Mary's card in dollars=____________
Write an equation to show that the two cards have the same amount of money left on them [don't know how to do this part.
To find the equation that shows that the two cards have the same amount of money =
Equation 1 = Equation 2
$90 - 15x = $110 - 20x
Collect like terms
-15x + 20x = $110 - $90
5x = 20
x = 20/5
x = 4
Hence, anytime Keith and Mary buys 4 pizzas their gift card will have the same amount of money left on them.
Central Park in New York City is shaped like a rectangle. On a map of the park in the coordinate plane, three of the vertices are located at (-1.25,-0.25) (-1.25, 0.25), and (1.25, 0.25). Distances on the map are in miles. What is the perimeter of Central Park? Show your work.
Answer: P = 6 miles
Step-by-step explanation: A rectangle is a quadrilateral with opposite sides with the same measure. As Central Park is one, its parallel sides has the same measurement.
Distance of points gives the measurement of the sides of the rectangle. It is calculated as:
[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]
For the first two points, (-1.25,-0.25) and (-1.25,0.25), note that x-components is the same, so, only y-component is relevant to the distance:
[tex]d=\sqrt{(-1.25+1.25)^{2}+(0.25+0.25)^{2} }[/tex]
[tex]d=\sqrt{(0.5)^{2} }[/tex]
d = 0.5
Two sides of the rectangle are 0.5 miles.
For points (-1.25,0.25) and (1.25,0.25), y-component will add 0 to the formula. Then,
[tex]d=\sqrt{(1.25+1.25)^{2}+(0.25-0.25)^{2} }[/tex]
[tex]d=\sqrt{(2.5)^{2}}[/tex]
d = 2.5
Two sides of the park are 2.5 miles.
Perimeter is the sum of all the sides of a geometric figure.
Perimeter of central Park is
P = 0.5+0.5+2.5+2.5
P = 6
Central Park has perimeter of 6 miles.
Solve the equation 0.3 = -15z.
Answer:
z = - 0.02
Step-by-step explanation:
0.3 = -15z
0.3 / -15 = z
-0.02 = z
Answer:
Z= - 0.02
Step-by-step explanation:
0.3=-15 *Z
Z= 0.3 / - 15
Z= - 0.02
Type a simplified fraction as an answer. PLEASE ANSWER ASAP!!!!
Answer:
0.06944444444 as a fraction equals 6944444444/100000000000
If f(x) = 3x-2, then f (8) - f (-5) =
Step-by-step explanation:
= f (8) - f (-5)
= 3*8-2 -(3*-5-2)
= 22-(-15-2)
= 22+17
= 39
Which equation represents a linear function? Equation 1: y = 2x + 1 Equation 2: y2 = 3x + 1 Equation 3: y = 5x5 − 1 Equation 4: y = 4x4 − 1 Equation 1 Equation 2 Equation 3 Equation 4
Answer:
Equation 1
Step-by-step explanation:
It does not have an x value with an exponent of 2 or greater.
Answer: I would think that equation 1 represents a linear function as it fllows the y= mx +b formula.
Step-by-step explanation: Linear functions sometimes use slope intercept form which is y = mx + b in this equation 2x would be your slope and 1 would be your y intercept.
7/10 divided by 5/10 Help 20 pts
Answer:
7/5
Step-by-step explanation:
ABCD is a parallelogram. If m∠CDA = 75, then what is m∠DAB? 95 75 105 115
Answer:
105 degrees.
Step-by-step explanation:
< DAB and <CDA are supplementary.
Therefore m < DAB = 180 - 75
= 105 degrees.
Answer:
105 degrees.
Step-by-step explanation:
What is the quotient of 8,592 ÷ 24
Answer:
358
Step-by-step explanation:
Answer:
358
Step-by-step explanation:
(See below for the picture of how to do it.)
The functions fand g are defined as follows. 3 f (x) = 3x - 5 g(x) = – 4x-1
Find f(-2) and g(?).
Simplify your answers as much as possible.
f(-2)= []
g(2)= []
Answer:
see below
Step-by-step explanation:
f (x) = 3x - 5
g(x) = – 4x-1
f(-2)=
Let x =-2
f(-2) = 3*-2 -5 = -6-5 = -11
g(2)=
Let x=2
g(2) = -4(2) -1 = -8-1 = -9
Answer:
[tex]\huge \boxed{\mathrm{f(-2)=-11 }} \\\\\\ \huge \boxed{\mathrm{g(2)=-9 }}[/tex]
Step-by-step explanation:
[tex]\sf f (x) = 3x - 5 \\\\\\ g(x)=-4x-1[/tex]
The input value or x value for f(-2) is -2.
[tex]\sf f (-2) = 3(-2) - 5 \\\\\\ \sf f (-2) = -6 - 5 \\\\\\ f(-2)=-11[/tex]
The input value or x value for g(2) is 2.
[tex]\sf g(2)=-4(2)-1 \\\\\\ g(2)=-8-1 \\ \\ \\ g(2)=-9[/tex]
pls help i give BRAINLIEST AND 50 POINTS
Answer:
60= per hour ....which is 1 hrs
so 120= 2 hrs
60+60
120
2hr is the answer
Answer:
3.5 hours
Step-by-step explanation:
[tex]speed \: = 60 \\ distance = 210 \\ time = \\ speed \: = \frac{distance}{time} [/tex]
[tex]time = \frac{distance}{speed} \\ time = \frac{210}{60} \\ time = \frac{7}{2} [/tex]
[tex]time = 3.5 \: hours[/tex]
Help me please! These are due today.
Answer:
[tex] {x}^{2} + 3x[/tex]
Step-by-step explanation:
1.
Area of shaded region = Area of external rectangle - Area of internal rectangle
[tex] = 4x(x + 2) - x(3x + 5) \\ = 4 {x}^{2} + 8x - 3 {x}^{2} - 5x \\ = 4 {x}^{2} - 3 {x}^{2} + 8x - 5x \\ = {x}^{2} + 3x \\ [/tex]
2.
Let the width of the rectangle be x inches.
Therefore, length of the rectangle = (x + 3) inches
A.
Area of rectangle
[tex] =(x + 3)\times x\\
=x^2 + 3x\\[/tex]
B.
Width of rectangle = 4 inches
Length of rectangle = 4 + 3 = 7 inches
Area of rectangle = 7*4 = 28 square inches.
Divide 200cm in the ratio 5:3
Answer:
125 cm and 75 cm
125:75 = 5:3
Step-by-step explanation:
Let the number be 5x and 3x
we are taking these value because in ratio
a:b = ax:bx
that is if we multiply both part of ratio by a same number ratio remains same.
____________________________________________________
Since we have divided 200 cm in two parts with value 5x and 3x
Thus,
sum of 5x and 3x will be equal to 200 cm
5x+3x = 200cm
8x = 200cm
x = 25 cm
Thus,
first part = 5x = 5*25 = 125 cm
other part = 3x = 3*25 = 75cm
Make a substitution to express the integrand as a rational function and then evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)
integral sqrt(x+36)*dx / x
Answer:
[tex]\mathbf{I =2{\sqrt{x+36}} + 6 \ In \begin {vmatrix} \dfrac{{\sqrt{x+36}}-6}{{\sqrt{x+36}}+6}\end {vmatrix}+ C}[/tex]
Step-by-step explanation:
Given that :
[tex]I = \int \dfrac{\sqrt{x+36}}{x} \dx = \int \dfrac{2u^2}{u^2-36} \ du[/tex]
x = u² - 36
Let u = [tex]\sqrt{x+36}[/tex]
Then:
[tex]du =\dfrac{1}{2 \sqrt{x+36}}dx[/tex]
[tex]2 \sqrt{x+36} \ \ du =dx[/tex]
[tex]2 u^2 \ \ du =dx[/tex]
[tex]\dfrac{2u^2}{u^2-36} \\ \\ 2u^2 \\ \\ 2u^2 - 72[/tex]
∴
[tex]I = \int 2 du + \int \dfrac{72}{u^2-36}\ du[/tex]
[tex]I = \int 2 du + 72 \int \dfrac{du}{u^2-6^2}[/tex]
[tex]I =2u+ 72 \times\dfrac{1}{2\times 6} \ In \begin {vmatrix} \dfrac{u-6}{u+6}\end {vmatrix}+ C[/tex]
[tex]I =2u + 6 \ In \begin {vmatrix} \dfrac{u-6}{u+6}\end {vmatrix}+ C[/tex]
substituting the value of u, we have:
[tex]\mathbf{I =2{\sqrt{x+36}} + 6 \ In \begin {vmatrix} \dfrac{{\sqrt{x+36}}-6}{{\sqrt{x+36}}+6}\end {vmatrix}+ C}[/tex]
There are 100 lockers in a school hallway and they are all closed. 100 students come through the hallway and start opening and closing lockers. The first student opened all the lockers The second student closed every second locker The 2nd, 4th,6th and so on were closed The third student changes the state of every 3rd locker. In other words the student visits lockers 3 6 9 and if the locker is open it gets closed. If it is closed it gets opened The fourth student changes the state of every fourth locker, the fifth student changes the state of every fifth locker and so on until the 100th student changes the state of the 100th locker Which lockers are open after all 100 students pass through the hallway
Answer:
1, 4, 9, 16, 25, 36, 49, 64, 81, and 100
Step-by-step explanation:
Let's pretend that the locker number is represented as a Binary (meaning it's either open or closed).
Looking at this, we can see that each locker is only acted upon if the student number is a factor of it. This is why the 3rd person changes the state of every 3 lockers, the 4th student changes the state of every 4 lockers, etc.
The factors of a number are the numbers that the original number is evenly divisible by. When we divide these, we also receive a factor. With this information, we can conclude that unless one of the factors is the square root of the number, then the "second divided by" factor is itself. For every other number, there will be a "second divided by" factor, so an even number of them. Because an even number + 1 = odd number, then only perfect squares will have an odd number of factors.
Hope this helped!
Answer:
The open lockers are:
1,4,9,16,25,36,49,64,81,100
Step-by-step explanation:
Note that locker 1 is opened by only the first student. So it stays open throughout.
Locker 2 is first opened by student 1, then closed by student 2. Other students don't touch it. So it stays closed.
Locker 3 is first opened by student 1, then closed by student 3. Other students don't touch it. So it stays closed.
Since 4 is a multiple of 1, 2, and 4, it is changed by the 1st, 2nd, and 4th students. Since there is an odd number (3) of changes, locker 4 stays open.
Observe that a locker at position n is opened by students with factors of n.
Every number can be written as the product of a pair of distinct numbers except perfect squares. For example, 6 can be written as 1 × 6 and 2 × 3. Hence, it has 4 factors, which means it is touched an even number of times, making it stay locked.
A number like 9 is written as 1 × 9 and 3 × 3. Hence, it has 3 factors, which is odd, making it stay open.
Since the perfect squares from 1 to 100 are 1,4,9,16,25,36,49,64,81,100, then the open lockers are:
1,4,9,16,25,36,49,64,81,100
g 1.32 Two points on a sphere of radius 3 are given as P1(3,0,30) and P2(3,45,45): (a) Find the position vectors of P1 and P2. (b) Find the vector connecting P1 (tail) to P2 (head). (c) Find the position vectors and the vector P1P2 in cylindrical and Cartesian coordinates.
Answer:
a) P.V of is OP₁ = [ 1.5i + 0j + 2.6k ], P.V of is OP₂ = [ 1.5i + 1.5j + 2.12k ]
b) Vector connecting P₁ to P₂ is [ 0i + 1.5j + 0.48k ]
c) cylindrical coordinates are (1.5, π/2, 0.48)
Step-by-step explanation:
Given that;
r = 3
P₁ ( 3, 0°, 30° ), P₂ ( 3, 45°, 45° )
a)
P.V of P₁
x = rcos∅sin∅ = 3(cos0°) ( sin30°) = (3 × 1 × 0.5) = 1.5
y = rsin∅sin∅ = 3(sin0°) (sin30°) = (3 × 0 × 0.5) = 0
z = rcos∅ = 3(cos30°) = ( 3 × 0.866) = 2.6
∴ P.V of is OP₁ = [ 1.5i + 0j + 2.6k ]
P.V of P₂
x = rcos∅sin∅ = 3(cos45°) ( sin45°) = (3 × 0.7071 × 0.7071) = 1.5
y = rsin∅sin∅ = 3(sin45°) (sin45°) = (3 × 0.7071 × 0.7071) = 1.5
z = rcos∅ = 3(cos45°) = ( 3 × 0.7071) = 2.12
∴ P.V of is OP₂ = [ 1.5i + 1.5j + 2.12k ]
b)
Vector connecting P₁ to P₂ is given by
OP₂ - OP₁ = [ 1.5i + 1.5j + 2.12k ] - [ 1.5i + 0j + 2.6k ]
= [ 0i + 1.5j + 0.48k ]
c)
P₁P₂ → = [ 0i + 1.5j + 0.48k ] = [ 1.5j + 0.48k ]
so in a cylindrical coordinate, it should be
r = √(o² + 1.5²) = 1.5
∅ = tan⁻¹[y/π] = π/2
z = 0.48
cylindrical coordinates are (1.5, π/2, 0.48)
What is the sum of the sixth terms of the geometric series 2-6+18-54+
Answer: 122
Step-by-step explanation:
Since it is a geometric sequence, lets see the pattern below:
-6÷2=-318÷-6=-3-54÷18=-3From this, we can see that we multiply each number by -3 to get the next number.
Before we find the sum, we first find the next number.
-54×-3=162
So the whole sequence will be: 2, -6, 18, -54, 162
Find the sum
2+(-6)+18+(-54)+162
=2-6+18-54+162
=-4-36+162
=-40+162
=122
Hope this helps!! :)
Please let me know if you have any question
Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving the plane region about the y-axis.
y = x3/2 y = 27 x = 0.
Volume of the solid generated by revolving the plane region about the y-axis is [tex]\frac{6561 \pi}{7}[/tex] .
Given, that y = x3/2, y = 27, x = 0
So, the volume of the solid generated by revolving the region about y axis will be,
[tex]V=\int_0^92\pi(x)(27-y)dx[/tex]
[tex]V=\int_0^92\pi x(27-x^{\frac{3}{2}})dx[/tex]
[tex]V=\left [ 27{\pi}x^2-\frac{4{\pi}x^\frac{7}{2}}{7} \right ]_0^9[/tex]
[tex]V=\left [ \frac{{\pi}\left(189x^2-4x^\frac{7}{2}\right)}{7} \right ]_0^9[/tex]
[tex]V=\frac{6561 \pi}{7}[/tex]
The image of the region bounded by plane is attached below.
Know more about volume of solid,
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The volume of the solid generated by revolving the plane region about the y-axis is approximately 6863.01 cubic units.
To use the shell method to find the volume of the solid generated by revolving the plane region about the y-axis, we need to express the limits of integration and the height of the infinitesimally thin cylindrical shells.
Given the equations:
y = x^(3/2)
y = 27
x = 0
To determine the limits of integration, we need to find the intersection points between the two curves: y = x^(3/2) and y = 27.
Setting the equations equal to each other:
x^(3/2) = 27
Taking the square root of both sides:
x = 27^(2/3)
x = 9
Therefore, the limits of integration are x = 0 and x = 9.
Now, let's consider an infinitesimally thin cylindrical shell with height "h" and radius "r" at some x value between 0 and 9.
The height of the shell, "h", is the difference between the y-values of the two curves:
h = 27 - x^(3/2)
The radius of the shell, "r", is the x-value.
The volume of the shell can be expressed as:
dV = 2πrh dx
To find the total volume, we integrate this expression from x = 0 to x = 9:
V = ∫[0, 9] 2π(27 - x^(3/2))x dx
Now, let's evaluate this integral:
V = 2π ∫[0, 9] (27x - x^(5/2)) dx
Integrating term by term:
V = 2π [(27/2)x^2 - (2/7)x^(7/2)] evaluated from 0 to 9
Plugging in the limits of integration:
V = 2π [(27/2)(9)^2 - (2/7)(9)^(7/2)] - 2π [(27/2)(0)^2 - (2/7)(0)^(7/2)]
Simplifying and evaluating the expression:
V = 2π [(27/2)(81) - (2/7)(3√(9))] - 0
V = 2π [1093.357] ≈ 6863.01 cubic units
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Given <1 and <2 are a linear pair, find the value of x if m<1 = 2x-5 and m<2 = 4x-7
This is geometry, and I need help because I don't know if it adds up to 90 or 180 degrees.
Answer:
32
Step-by-step explanation:
Linear pair means they form a line, or add to 180°.
2x − 5 + 4x − 7 = 180
6x − 12 = 180
6x = 192
x = 32
Imagine that Amy counted 60 numbers per minute and continued to count nonstop until she reached 19,000. Determine a reasonable estimate of the number of hours it would take Amy to complete the counting It will take Amy approximately hours to count to 19,000. (Type a whole number)
Answer:
It will take ≈5 hours (5.278)
Step-by-step explanation:
First we need to find how many number she counts in one hour. We know she counts 60 every one minute and there are 60 minutes in an hour. 60x60=3600
Now we divide 19,000 by 3600 to find how many hours it will take
19000/3600=5.278
It will take ≈5 hours (5.278)
what's the answer for p2 when p=25
Answer: p^2 = 25 ^2 = 625
Plz help (URGENT) The data shows the number of bacteria in a culture after a given number of hours. Based on the data, which is closest to the number of hours it takes the culture to reach 12,000 bacteria? A) 16 hours B) 19 hours C) 22 hours D) 25 hours Hour Bacteria 1 2,215 2 2,235 3 2,360 4 2,680 5 3,075
Answer:
The number of hours it takes the culture to reach 12,000 bacteria is 41 hours.
Step-by-step explanation:
To predict the number of hours it takes to culture a certain number of bacteria form a regression equation of number of hours (y) based on the number of bacteria (x) using the provided data.
The general form of the regression equation is:
[tex]y=a+bx[/tex]
Compute the values of a and b as follows:
[tex]a=\frac{\sum Y\cdot\sum X^{2}-\sum X\cdot\sum XY}{n\cdot \sum X^{2}-(\sum X)^{2}}=\frac{15\cdot 32109075 - 12565\cdot 39860}{5\cdot 32109075-(12565)^{2}}=-7.203\\\\b=\frac{n\cdot \sum XY-\sum X\cdot\sum Y}{n\cdot \sum X^{2}-(\sum X)^{2}}=\frac{5\cdot 39860- 12565\cdot 15}{5\cdot 32109075-(12565)^{2}}=0.004[/tex]
*Use the Excel data sheet attached.
The regression equation of number of hours based on the number of bacteria is:
[tex]y=-7.203+0.004x[/tex]
Compute the number of hours it takes the culture to reach 12,000 bacteria as follows:
[tex]y=-7.203+0.004x[/tex]
[tex]=-7.203+(0.004\times 12000)\\=-7.203+48\\=40.797\\\approx 41[/tex]
Thus, the number of hours it takes the culture to reach 12,000 bacteria is 41 hours.
Solve the equation for x and enter your answer in the box below.
x - 3x + 4 = 3 - 9
X = Answer
HINT
SUBMIT
th
Answer:
I think that it's either x= -2 or x= 0.5
Step-by-step explanation:
x=5 is the value of equation x - 3x + 4 = 3 - 9.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is x - 3x + 4 = 3 - 9
x minus three times of x plus four equal to three minus nine
In the given equation x is the variable and we need to solve the value of x.
x - 3x + 4 = 3 - 9
Add the like terms
-2x+4=-6
Subtract 4 from both sidees
-2x=-10
Divide both sides by -2
x=5
Hence, x=5 is the value of equation x - 3x + 4 = 3 - 9.
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What is -1 ⅓ × -⅖
Please explain your answer and show your work.
Answer:
[tex]\frac{8}{15}[/tex]
Step-by-step explanation:
Change the mixed number into an improper fraction: -1 × 3 = -3, -3 + 1 = -2. Put -2 over 3: [tex]\frac{-2}{3}[/tex] Multiply -2/3 and -2/5: [tex]\frac{-2}{3}[/tex] × [tex]-\frac{2}{5}[/tex] = [tex]\frac{8}{15}[/tex]Therefore, the answer is [tex]\frac{8}{15}[/tex].
Weights and heights of turkeys tend to be correlated. For a population of turkeys at a farm, this correlation is found to be 0.64. The average weight is 17 pounds, SD is 5 pounds. The average height is 28 inches and the SD is 8 inches. Weight and height both roughly follow the normal curve. For each part below, answer the question or if not possible, indicate why not. A turkey at the farm which weighs more than 90% of all the turkeys is predicted to be taller than % of them. The average height for turkeys at the 90th percentile for weight is Of the turkeys at the 90th percentile for weight, roughly what percent would you estimate to be taller than 28 inches?
Answer:
a turkey at the farm which weighs more than 90% of all the turkeys is predicted to be taller than 79.37 % of them.
The average height for turkeys at the 90th percentile for weight is 34.554
Of the turkeys at the 90th percentile for weight, roughly the percentage that would be taller than 28 inches 79.37%
Step-by-step explanation:
The data given for the study can be listed as follows
For a population of turkeys at a farm, the correlation found between the weights and heights of turkeys is r = 0.64
[tex]\overline x[/tex] = 17 (i . e the average weight in pounds)
[tex]S_x[/tex] = 5 ( i . e the standard deviation of the weight in pounds)
[tex]\overline y[/tex] = 28 (i . e the average height in inches)
[tex]S_y[/tex] = 8 ( i . e the standard deviation of the height in inches)
The slope of the regression line can be expressed as :
[tex]\beta_1 = r \times ( \dfrac{S_y}{S_x})[/tex]
[tex]\beta_1 = 0.64 \times ( \dfrac{8}{5})[/tex]
[tex]\beta_1 = 0.64 \times 1.6[/tex]
[tex]\beta_1 = 1.024[/tex]
Similarly the intercept of the regression line can be estimated by using the formula:
[tex]\beta_o = \overline y - \beta_1 \overline x[/tex]
replacing the values, we have:
[tex]\beta_o = 28 -(1.024)(17)[/tex]
[tex]\beta_o = 28 -17.408[/tex]
[tex]\beta_o = 10.592[/tex]
However, the regression line needed for this study can be computed as:
[tex]\hat Y = \beta_o + \beta_1 X[/tex]
[tex]\hat Y = 10.592 + 1.024 X[/tex]
Recall that;
both the weight and height roughly follow the normal curve
Thus, the weight related to 90th percentile can be determined as shown below.
Using the Excel Function at 90th percentile, which can be computed as:
(=Normsinv (0.90) ; we have the desired value of 1.28
∴
[tex]\dfrac{X - \overline x}{s_x } = (Normsinv (0.90))[/tex]
[tex]\dfrac{X - \overline x}{s_x } = 1.28[/tex]
[tex]\dfrac{X - 17}{5} = 1.28[/tex]
[tex]X - 17 = 6.4[/tex]
X = 6.4 + 17
X = 23.4
The predicted height [tex]\hat Y = 10.592 + 1.024 X[/tex]
here; X = 23.4
[tex]\hat Y = 10.592 + 1.024 (23.4)[/tex]
[tex]\hat Y = 10.592 + 23.9616[/tex]
[tex]\hat Y = 34.5536[/tex]
So the probability of predicted height less than 34.5536 can be expressed as:
[tex]P(Y < 34.5536) = P( \dfrac{Y - \overline y }{S_y} < \dfrac{34.5536-28}{8})[/tex]
[tex]P(Y < 34.5536) = P(Z< \dfrac{6.5536}{8})[/tex]
[tex]P(Y < 34.5536) = P(Z< 0.8192)[/tex]
From the Z tables;
P(Y < 34.5536) =0.7937
Thus, a turkey at the farm which weighs more than 90% of all the turkeys is predicted to be taller than 79.37 % of them.
The average height for turkeys at the 90th percentile for weight is :
[tex]\hat Y = 10.592 + 1.024 X[/tex]
here; X = 23.4
[tex]\hat Y = 10.592 + 1.024 (23.4)[/tex]
[tex]\hat Y = 10.592 + 23.962[/tex]
[tex]\mathbf{\hat Y = 34.554}[/tex]
Of the turkeys at the 90th percentile for weight, roughly what percent would you estimate to be taller than 28 inches?
This implies that :
P(Y >28) = 1 - P (Y< 28)
[tex]P(Y >28) = 1 - P( Z < \dfrac{28 - 34.554}{8})[/tex]
[tex]P(Y >28) = 1 - P( Z < \dfrac{-6.554}{8})[/tex]
[tex]P(Y >28) = 1 - P( Z < -0.8193)[/tex]
From the Z tables,
[tex]P(Y >28) = 1 - 0.2063[/tex]
[tex]\mathbf{P(Y >28) = 0.7937}[/tex]
= 79.37%
The price of a car has been reduced from $21,000 to $13,230. What is the percentage decrease of the price of the car?
4 lines extend from point B. A line extends straight up from B to point A. Another line extends up and to the right to point C. Another line extends slight up and to the right to point D. The other line extends slightly down and to the right to point E.
Given that ∠ABC ≅ ∠DBE, which statement must be true?
∠ABC ≅ ∠ABD
∠ABD ≅ ∠CBE
∠CBD ≅ ∠DBE
∠CBD ≅ ∠ABC
Answer:
The Correct Answer Is: ∠ABD ≅ ∠CBE
Step-by-step explanation:
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∠ABD≅∠CBE is the true statement of congruent angles as per the given condition ∠ABC ≅∠DBE.
What are congruent angles?" Congruent angles are pair of such angles which are equal in their measurements."
According to the question,
Given,
∠ABC ≅∠DBE ________(1)
As shown in the diagram drawn as per the given conditions we have,
'D' is the interior point of angle ABC.
Therefore,
∠ABC = ∠ABD + ∠CBD ______(2)
'C' is the interior point of ∠DBE.
Therefore,
∠DBE = ∠CBD + ∠CBE ______(3)
Substitute (2) and (3) in (1) to represent congruent angles we get,
∠ABD + ∠CBD ≅ ∠CBD + ∠CBE
⇒∠ABD ≅ ∠CBE (∠CBD is common in both)
Hence, ∠ABD≅∠CBE is the true statement of congruent angles as per the given condition ∠ABC ≅∠DBE.
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Which trigonometric inequality has no solution over the interval 0<=x<=2 a. csc(x)1>0 b.cos(x)-1>0 c.cot(x)-1>0 d.tan(x)-1>0
Answer:
B
Step-by-step explanation:
a. csc x − 1 > 0
csc x > 1
sin x < 1
x = [0, π/2) U (π/2, 2]
b. cos x − 1 > 0
cos x > 1
x = no solution
c. cot x − 1 > 0
cot x > 1
tan x < 1
x = [0, π/4) U (π/2, 2]
d. tan x − 1 > 0
tan x > 1
x = (π/4, π/2) U (π/2, 3π/4)
Of the 4 options, only B has no solution.
The only inequality that does not have a solution with the range is option B; cos x − 1 > 0.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
A. csc x − 1 > 0
csc x > 1
sin x < 1
x = [0, π/2) U (π/2, 2]
B. cos x − 1 > 0
cos x > 1
x = no solution
C. cot x − 1 > 0
cot x > 1
tan x < 1
x = [0, π/4) U (π/2, 2]
D. tan x − 1 > 0
tan x > 1
x = (π/4, π/2) U (π/2, 3π/4)
Therefore option B is the only inequality that does not have a solution with the range.
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Triangle ABC has side lengths of 3 and 10. What are the restrictions on the third side?
Answer:
7 < third side < 13
Step-by-step explanation:
The triangle inequality requires the sum of the shortest two side lengths to be more than the longest side length. The effect of that is to limit the third side to values between the sum and difference of the other two sides:
7 < third side < 13