The distances in feet covered in 4 steps, 6 steps, 12 steps, and 30 steps are 10 feet, 15 feet, 30 feet and 75 feet.
Missing informationWhen you walk with a normal stride, the average distance covered in 2 steps is about 5 feet
How to determine the distances?From the question, we have:
Rate = 5 feet per 2 steps
This gives
Rate = 5/2 feet per step
So, we have:
Rate = 2.5 feet per step
The distance is then calculated as:
Distance = Rate * Steps
This gives
Distance = 2.5 * Steps
So, the distances in feet covered in 4 steps, 6 steps, 12 steps, and 30 steps are
Distance = 2.5 * 4 = 10 feet
Distance = 2.5 * 6 = 15 feet
Distance = 2.5 * 12 = 30 feet
Distance = 2.5 * 30 = 75 feet
Hence, the distances in feet covered in 4 steps, 6 steps, 12 steps, and 30 steps are 10 feet, 15 feet, 30 feet and 75 feet.
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Fill in the blank. In the triangle below, x=?. Round your answer to two decimal places.
Answer:
x = 31.5, y = 41.7, z = 48
Step-by-step explanation:
use the rule that cos (x) = adjacent/hypotenuse:
you know that x (the angle) = 42 and the adjacent side = 35, so:
cos (42) = 35/y
y = 35/cos(42)
y = 47.1
then, to find x:
use the fact that tan (x) = opposite side/adjacent side
so tan (42) = x/35
x = 35tan(42)
x = 31.5
finally, you know all 3 angles of the triangle have to add up to 180, so to find z you can do:
z + 90 + 42 = 180
z + 132 = 180
z = 48
3. College Students (10 points)
In Fall 2019, there were approximately 16.6 million undergraduate students in degre
granting postsecondary institutions. This represents a 5% decrease from the Fall 200
number of students. How many undergraduate students were there in 2009?
Source: https://nces.ed.gov/fastfacts
The number of students is 33.2 million
What is percentage decrease?Percent decrease refers to the percent change in the value when it is decreased over a period of time. Percentage decrease expresses the decrease in the given value with respect to its initial value in the form of a percentage.
Given:
In 2019= 16.6 million
% decrease = 5%
So,
% decrease= x - 16.6/ x
5% = x- 16.6/x
0.05= (x-16.6)/x
0.05x = x-16.6
-0.05 x = -16.6
x= 16.6/0.05
x= 16600000/0.05
x= 332,000,000
x= 33.2 million.
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Find the equation of the line that
3
is perpendicular to y ===x+1
and contains the point (9,12).
4
4
Y = 3 x + [ ? ]
Step-by-step explanation:
ATTACHED IS THE SOLUTION!!Determine whether it is a function
Answer:
Relation 3 is not a function, as s has two outputs: tree and desk. Relation 4 is not a function for the same reason. -1 has three outputs: -2, -4, and -7.
Match each quadratic equation with its roots.
a2-a+11=0
a2-2a+15=0
a = 1ti√14
1± √47
a= 2
a=
1+√43
2
a=1+3i
a2-2a+10=0
a2-a+12=0
30
Answer:
wrong question please place correctly thanks
what type of expression is 3+7-1/2
Numerical Expression
The expression consists of numbers and arithmetic operators. It does not contain equality or inequality symbols.
find the common denominator and thin combine the numerators over the common denominator trhin simplify each term thin simplify by adding subtracing thin the result can be shown in multiple forms
exact form 19/2
decimal form 9.5
mixed number form 9 1/2
find sin(x/2), cos (x/2), and tan(x/2) from the given information.
Sin(x)= 15/17, 0 < x <90
sin(x/2)= ?
cos(x/2)=?
tan(x/2)= 0.6
I need help with sin and cos. I know what tan is.
Step-by-step explanation:
sin(x/2) = sqrt((1 - cos(x))/2)
cos(x/2) = sqrt((1 + cos(x))/2)
tan(x/2) = sin(x/2)/cos(x/2)
sin(x) = 15/17
so, we can assume the Hypotenuse of the right-angled triangle is 17, the vertical leg is 15.
via Pythagoras we get the 3rd, horizontal side :
17² = 15² + side²
289 = 225 + side²
64 = side²
side = 8
cos(x) = 8/17
sin(x/2) = sqrt((1 - 8/17)/2) = sqrt(9/34) = 3/sqrt(34) =
= 0.514495755...
cos(x/2) = sqrt((1 + 8/17)/2) = sqrt(25/34) = 5/sqrt(34) =
= 0.857492926...
tan(x/2) = 3/sqrt(34) / 5/sqrt(34) = 3/sqrt(34) × sqrt(34)/5 =
= 3/5 = 0.6
Help please confused
Answer:
AB : y=1/5x+12
CB : y=-3x+10
CD : y=1/2x-1
DA : y=-2x+1
I have a geometry question thank you!
Answer:
The answer is 1.5.
Step-by-step explanation:
I don't have one
In a recent year (365 days), a hospital had 5705
births.
a. Find the mean number of births per day.
b. Find the probability that in a single day, there are 17
births.
c. Find the probability that in a single day, there are no births. Would 0 births in a single day be a significantly low number of births?
Using the Poisson distribution, it is found that:
a) The mean is of 15.63.
b) The probability is of 0.0911 = 9.11%.
c) The probability is [tex]e^{-15.63}[/tex], which is less than 0.05, hence 0 births in a single day would be a significantly low number of births.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successes.e = 2.71828 is the Euler number.[tex]\mu[/tex] is the mean in the given interval.Item a:
The mean is given by:
[tex]\mu = \frac{5705}{365} = 15.63[/tex]
Item b:
The probability is P(X = 17), hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 17) = \frac{e^{-15.63}(15.63)^{17}}{(17)!} = 0.0911[/tex]
The probability is of 0.0911 = 9.11%.
Item c:
The probability is P(X = 0), hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-15.63}(15.63)^{0}}{(0)!} = e^{-15.63}[/tex]
The probability is [tex]e^{-15.63}[/tex], which is less than 0.05, hence 0 births in a single day would be a significantly low number of births.
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Using the Poisson distribution, it is found that
a) The mean is 15.63.
b) The probability is[tex]e^{-15.63}[/tex] of 0.0911 = 9.11%.
c) The probability is, which is less than 0.05, hence 0 births in a single day would be a significantly low number of births.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P\left(X=x\right)=\frac{e^{-\mu }\mu ^x}{x!}[/tex]
The parameters are
x is the number of successes.
e = 2.71828 is the Euler number.
[tex]\mu[/tex] is the mean in the given interval.
Item a:The mean is given by:
[tex]\:\mu =\frac{5705}{365}[/tex]
Item b: The probability is P(X = 17), hence:
[tex]P\left(X=17\right)=\frac{e^{-15.63\:}\left(15.63\right)\:^{17}}{17!}=0.0911[/tex]
The probability is of 0.0911 = 9.11%.
Item c:The probability is P(X = 0), hence:
[tex]P\left(X=0\right)=\frac{e^{-15.63\:}\left(15.63\right)\:^{0}}{0!}=e^{-15.63}[/tex]
The probability is,[tex]e^{-15.63}[/tex] which is less than 0.05,
hence 0 births in a single day would be a significantly low number of births.
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You invest $2100 in an account at 1.5% per year simple interest. The equation
that represents this scenario is:
A(n) = 2100 + (n-1)(0.0152100)
How much will you have in the account in year 6? Round your answer to the
nearest dollar.
OA. $2289
о C. $2258
D. $2132
B. $17,850
Answer:
My guess would be D
Step-by-step explanation:
Which of the numbers below are whole numbers?
A. 546
B. 7317
C. 1/3
D. 47
E. 93.3.
F. 907.68
(x³ + ³) / (x - y)
Do not include parentheses in your answer.
The simplified expression of [tex]\frac{x^3 + (-y)^3}{(x - y}[/tex] is [tex]x^2+xy+y^2[/tex]
Complete questionSimplify the expression: (x³ + (-y)³) / (x - y)
Do not include parentheses in your answer.
How to simplify the expression?The expression is given as:
[tex]\frac{x^3 + (-y)^3}{(x - y}[/tex]
Open the inner bracket
[tex]\frac{x^3 -y^3}{(x - y}[/tex]
Apply the difference of two cubes to the numerator
[tex]\frac{(x-y)(x^2+xy+y^2)}{(x - y}[/tex]
Cancel out the common factors
[tex]x^2+xy+y^2[/tex]
Hence, the simplified expression of [tex]\frac{x^3 + (-y)^3}{(x - y}[/tex] is [tex]x^2+xy+y^2[/tex]
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pls help me solve for x in this equation
Answer:
x = 9/2
Step-by-step explanation:
√2x + √2x = 6
2√2x = 6
2√2x/2 = 6/2
√2x = 3
(√2x)² =( 3)²
2x = 9
x = 9/2
Answer:
x = 4.5
Explanation:
[tex]\rightarrow \sf \sqrt{2x} + \sqrt{2x} = 6[/tex]
add following
[tex]\rightarrow \sf 2\sqrt{2x} = 6[/tex]
divide both sides by 2
[tex]\rightarrow \sf \sqrt{2x} = 3[/tex]
square both sides
[tex]\rightarrow \sf 2x = 3^2[/tex]
simplify the following
[tex]\rightarrow \sf 2x = 9[/tex]
divide both sides by 2
[tex]\rightarrow \sf x = 4.5[/tex]
If the length of rectangle is thrice of its breadth and it's perimeter is 32 cm then finds its area.
Answer:
48 cm²
Explanation:
Let the breadth be b, then the length is 3b
P = 2(Length + Breadth)
32 = 2(3b + b)
32 = 2(4b)
8b = 32
b = 4
Breadth is 4 cm
Length: 3b = 3(4) = 12 cm
Area of rectangle:
Length × Breadth
12 × 4
48 cm²
Given :-
Length of rectangle is thrice of its breadth.Its perimeter is 32 cm.To Find :-
Area of rectangle?Solution :-
Let breadth of rectangle be x cm As it is stated in question that length of rectangle is thrice its breadth so length of rectangle will be 3x cmUsing formula;
Perimeter of rectangle = 2(L + B)Where;
L denotes length of rectangleB denotes a breadth of rectangleWe have;
Perimeter of rectangle = 32 cmLength of rectangle (L) = 3xBreadth of rectangle (B) = xBy putting all values in formula we get;
→ 2(3x + x) = 32
→ 2(4x) = 32
→ 2 × 4x = 32
→ 8x = 32
→ x = 32/8
After dividing 32 with 8, we get;
→ x = 4
Hence;
Length (L) = 3x = 3 × 4 = 12 cmBreadth (B) = x = 4 cmNow, using formula;
Area of rectangle = L × BWhere;
L denotes length of rectangleB denotes a breadth of rectangleWe have;
Length of rectangle (L) = 12 cmBreadth of rectangle (B) = 4 cmArea of rectangle = ?By putting all values in formula we get;
→ Area of rectangle = 12 × 4
By multiplying 12 with 4, we get;
→ Area of rectangle = 48 cm²
Hence, area of rectangle is 48 cm².Pls ,see the attachment
A baby weighed only 8.7 ounces at birth. How much lighter was she than an average baby, who weighs about 7 lb 8 ounces?
The baby is 111.3 ounces or 6.96 pounds lighter than an average baby.
What is weight ?Weight is the measurement of Gravitational force on an object.
It can be zero as in the space.
It is given in the question that
A baby weighed only 8.7 ounces at birth
weight of an average baby is 7lb 8 ounces
1 lb = 16 ounce
an average baby weight = 7 * 16 +8 = 120 ounces
The baby weight is just 8.7 ounces
so the baby is 120-8.7 = 111.3 ounces lighter than an average baby.
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Please help with this difficult one...
The composite function is given as follows:
[tex](f \circ g)(x) = \frac{2x + 6}{3x + 22}[/tex]
The domain of the composite function is: [tex]\mathbb{R} - \left\{-\frac{22}{3}, 3\right\}[/tex]
What is the composite function of f(x) and g(x)?The composite function is given by:
[tex](f \circ g)(x) = f(g(x))[/tex]
In this problem, the functions are:
[tex]f(x) = \frac{2}{x + 3}[/tex].[tex]g(x) = \frac{13}{x + 3}[/tex].Hence the composite function is:
[tex](f \circ g)(x) = f\left(\frac{13}{x + 3}\right) = \frac{2}{\frac{13}{x + 3} + 3} = \frac{2(x + 3)}{13 + 3(x + 3)} = \frac{2x + 6}{3x + 22}[/tex]
For the domain, we have to remove the points outside the domain of both the primitive and the composite functions, that is, the zeroes of the denominators, hence:
[tex]x + 3 \neq 0 \rightarrow x \neq 3[/tex]
[tex]3x + 22 \neq 0 \rightarrow x \neq -\frac{22}{3}[/tex]
Hence the domain is:
[tex]\mathbb{R} - \left\{-\frac{22}{3}, 3\right\}[/tex]
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Managerial Accounting
Answer:
1400 units
$26,600
1700 units
$32,300
Step-by-step explanation:
yw :))
Which of the following can be the sides of right triangle? (A) 5cm, 8cm, 17cm (B) 8cm, 15cm, 17cm
Answer:
B) 8cm, 15cm, 17cm
Step-by-step explanation:
We will use angle sum property for this question. (Angle sum property means the addition of the 2 smallest sides have to be larger or equal to the biggest side)
We will try it with all the options.
Option A) 5+8=13. Which is not greater then 17 so it cant be a right triangle.
Option B) 8+15=23. Which is greater then 17 so it can be a right triangle
Hope I helped
find the slope of the line that passes through the points (2,1) and (-7,4)
Answer:
[tex]-\frac13[/tex]
Step-by-step explanation:
Just the slope, so we can simply apply the definition, as variation in y over the variation in x
[tex]m= \frac{\Delta y}{\Delta x} = \frac{1-4}{2-(-7)} = \frac {-3}{9} = -\frac13[/tex]
Answer:
0.222
Step-by-step explanation:
Y2-Y1 ÷ X2-X1
4-2 ÷ -7-2
2÷-9
0.222
\frac{7}{4x}+\frac{5}{4x^2}
4x
7
+
4x
2
5
The expression given can be written as [tex]\rm \dfrac{(16x^2 + 35 )}{28x^2}[/tex]
What is Expression ?Expression is a mathematical statement consisting of variables , constants and mathematical operators .
It is given in the question to solve the expression
[tex]\rm \dfrac{4x}{7} + \dfrac{5}{4x^2}[/tex]
Taking LCM , LCM = 28x²
[tex]\rm \dfrac{(16x^2 + 35 )}{28x^2}[/tex]
Therefore the expression given can be written as [tex]\rm \dfrac{(16x^2 + 35 )}{28x^2}[/tex]
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(x) = x + 0.14x, then find the value of T(290).
A. 300.45
B. 351.2
C. 325.8
D. 330.6
Answer:
D. 330.6
Step-by-step explanation:
To evaluate the function for a specific value of x, put that value where x is in the function definition, and do the arithmetic.
__
T(x) = x +0.14x . . . . . given function definition
T(290) = 290 +0.14×290 = 290 +40.6 . . . . substitute 290 for x
T(290) = 330.6
The value of T(290) will be 330.6.The relation between them is shown as T(x) is dependent and x is the independent variable. Option D s correct.
What is a function?A connection between independent variables and the dependent variable is defined by the function.
Functions help to represent graphs and equations. A function is represented by the two variables one is dependent and another one is an independent function.
Given relation;
T(x) = x +0.14x
Substitute the value of x we get;
T(290) = 290 +0.14×290
T(290) = 330.6
Hence, option D s correct.
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f(x) = 3x² + 5; find f(x + 3) - [f(x) + 3]
Answer: 18x+24
Step-by-step explanation:
[tex]f(x+3)=3(x+3)^2 + 5\\\\f(x+3)=3(x^2 + 6x+9)+5\\\\f(x+3)=3x^2+18x+27+5\\\\f(x+3)=3x^2 + 18x+32[/tex]
[tex]\therefore f(x+3)-[f(x)+3]=(3x^2 +18x+32)-[3x^2 +5+3]\\ \\=3x^2 +18x+32-3x^2 - 8\\\\=\boxed{18x+24}[/tex]
If function f(x) = 3x² + 5 then the value of f(x + 3) - [f(x) + 3] is 18x + 24.
Given the function f(x) = 3x² + 5.
We have to find the value of f(x + 3) - [f(x) + 3]
First we have to find the value of f(x + 3) - [f(x) + 3]
f(x + 3) = 3 (x + 3) ² + 5f(x + 3)
= 3(x ² + 6x + 9) + 5f(x + 3)
= 3x ² + 18x + 27 + 5f(x + 3)
= 3x ² + 18x + 32
Now substitute these values and find the value of f(x + 3) - [f(x) + 3].
f(x + 3) - [f(x) + 3] = (3x² + 18x + 32) - [3x ^ 2 + 5 + 3]
=3x ² + 18x + 32 - 3x ² - 8
=18x + 24
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the ufugfldldd
5+9x+3gg3g3\
1 b
Select all radical expressions that are equivalent to...
Answer:
B AND E
Step-by-step explanation:
hope that helpsndbwbe
What is the y-intercept of the equation of the line that is perpendicular to the line y = 3/5x + 10 and passes through the point (15, –5)? The equation of the line in slope-intercept form is y =-5/3 x + ____
Substituting into point-slope form,
[tex]y+5=-\frac{5}{3}(x-15)\\\\y+5=-\frac{5}{3}x+25\\\\\boxed{y=-\frac{5}{3}x+20}[/tex]
7. What is the ratio of the interior angles of a pentagon and a decagon?
Answer:
A pentagon has 5 sides.
Sum of the interior angles = ( n - 2) x 180
Sum of the interior angles = ( 5 - 2) x 180
Sum of the interior angles = 540°
STEP 2: Find one interior angle:
one interior angle = 540 ÷ 5 = 108°
STEP 3: Find the sum of interior angles of a decagon
A decagon has 10 sides
Sum of the interior angles = ( n - 2) x 180
Sum of the interior angles = ( 10 - 2) x 180
Sum of the interior angles = 1440°
STEP 4: Find one interior angle:
one interior angle = 1440 ÷ 10 = 144°
STEP 5: Find the ratio:
Pentagon : Decagon = 108 : 144
Simplify:
Pentagon : Decagon = 3 : 4
Answer: The ratio is 3 : 4
Consider the function f(x)=3^x and the translation if f(x) named g(x). Janeen created a table for select values of x. What can be concluded about the relationship between two functions?
The conclusion about the relationship is
The functions have the same base.The functions have the same range.The functions have the same domain.g(x) is a translation left 1 unit.What is function?The complete question is:
Consider the function f(x) = 3x and a translation of f(x) named g(x). Janeen created a table for select values of x. Her table is shown below. What can be concluded about the relationship between the two functions? Check all that apply.
The functions have the same base.
The functions have the same range.
The functions have the same exponent.
The functions have the same domain.
g(x) is a translation left 1 unit.
g(x) is a translation right 2 units.
g(x) is a translation up 2 units.
Given function is:
f(x) = [tex]3^{x}[/tex]
g(x) = [tex]3^{x+1}[/tex]
Firstly, the functions have the same base i.e., base 3.
second, the functions have the same range.
As the range of f are all the values that f can assume. i.e., positive numbers and the range of g are all the values that g can assume. i.e., positive numbers.
third, both functions have the same domain as x = {0,1,2,3}.
Fourth, g(x) = f(x+1). So, g(x) is a translation left 1 unit.
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1. Given GH = 7x + 3, HI= 3x - 5,
and GI= 9x + 5.
H
G
A. Find x:
B. Find GH:
Answer:
[tex]\boxed{\bf x=7}[/tex]
[tex]\boxed{\bf GH= 52}[/tex]
Step-by-step explanation:
In the line segment..
[tex]\bf 7x+3+3x-5=9x+5[/tex]
Combine like terms.
[tex]\bf 10x-2=9x+5[/tex]Add -2 to both sides.
[tex]\bf 10x-2+2=9x+5+2[/tex][tex]\bf 10x=9x+7[/tex]Subtract 9x from both sides.
[tex]\bf 10x-9x=9x+7-9x[/tex][tex]\boxed{\bf x=7}[/tex][tex]\bf GH=7x+3[/tex]
[tex]\bf 7(7)+3[/tex][tex]\bf 49+3[/tex][tex]\boxed{\bf 52}[/tex]__________________