Answer:
7
Step-by-step explanation:
Here we have the hypotonouse and an angle
we are looking for the side opposite to the angle
this means we should use SOH
sin(26)=(x/16)
16*sin(26)=x
x=7.01393
which is closest to 7
There is money to send four of nine city council members to a conference in Honolulu. All want to go, so they decide to choose the members to go to the conference by a random process. How many different combinations of four council members can be selected from the nine who want to go to the conference
Answer:
126
Step-by-step explanation:
There are 9 city council members.
We have to choose 4 of them.
We have to use the combination as :
[tex]$^9C_4$[/tex]
where, 9 is the population size
4 is the sample size.
Therefore, the total number of possible samples without replacement is given as :
[tex]$^9C_4=\frac{9!}{4!(9-4)!}$[/tex]
[tex]$=\frac{9!}{5! \ 4!}$[/tex]
[tex]$=\frac{9 \times 8 \times 7 \times 6}{4 \times 3 \times 2 \times 1}$[/tex]
= 126
(b) If A(t) is the amount of the investment at time t for the case of continuous compounding, write a differential equation satisfied by A(t).
Answer:
[tex]A'(t) = rA(t)[/tex]
Step-by-step explanation:
Given
[tex]A(t) \to[/tex] Amount
Required
The differential equation
The equation for the amount is:
[tex]A(t) = A_0 * e^{rt}[/tex]
Where:
[tex]A_0 \to[/tex] initial amount
[tex]r \to[/tex] rate
[tex]t \to[/tex] time
Differentiate[tex]A(t) = A_0 * e^{rt}[/tex]
[tex]A'(t) = A_0 * r * e^{rt}[/tex]
So, we have:
[tex]A'(t) = rA_0 * e^{rt}[/tex]
From the question, we have: [tex]A(t) = A_0 * e^{rt}[/tex]
So, the equation becomes
[tex]A'(t) = rA(t)[/tex]
PLEASE ANSWER!! I don’t understand
Answer:
[tex]m\angle 2=122^{\circ},\\m\angle 1 = 58^{\circ}[/tex]
Step-by-step explanation:
By definition, tangent lines touch a circle at one point. This one point intersects the circle at a 90 degree angle.
In any circle, the measure of an inscribed angle is exactly half of the arc it forms. Since [tex]\angle 2[/tex] forms an arc labelled 244 degrees, the measure of angle 2 must be [tex]\frac{244}{2}=\boxed{122^{\circ}}[/tex].
Angle 1 and 2 form one side of a line. Since there are 180 degrees on each side of the line, we have:
[tex]\angle 1+\angle 2=180,\\\angle 1 + 122=180,\\\angle 1=180-122=\boxed{58^{\circ}}[/tex]
In ΔOPQ, the measure of ∠Q=90°, OQ = 39, QP = 80, and PO = 89. What ratio represents the cosine of ∠P?
Answer:
The cosine of angle P = opposite / adjacent = 39 / 80
Step-by-step explanation:
Pls help ASAP
Compare and contrast how to graph: x=2 and y= -4
Answer:
plotting x = 2
see the x- axis look for the point x = 2(on right side of the origin ). Mark that point and draw a straight line parallel to the y- axis.
This is the graph of x = 2
plotting y = -4
see the y- axis and then look for the point y= -4 (that must be 4 units below the origin). Mark that point and draw a straight line parallel to the x- axis.
This is the graph of y = -4
we see that, the graph x = 2 is parallel to the y-axis whereas the graph y = -4 is parallel to the x- axis.
Ardi and Lei are both travelling by train.
Ardi's train travels 70 km in 35 minutes.
Lei's train travels 585 km.
It leaves at 9:05 and arrives at 13:35.
Work out the difference, in km/h, between the average speed of their trains.
Answer:
10 kilometer/hour
Step-by-step explanation:
Average speed = Total distance travelled / Total time taken
Ardi:
Total distance travelled = 70 km
Total time taken = 35 minutes = 35/60 hour
Average speed = Total distance travelled / Total time taken
= 70 km ÷ 35/60 hr
= 70 × 60/35
= 4,200/35
= 120 kilometer/hour
Lei:
Total distance travelled = 585 km Total time taken = 9:05 - 13:35 = 4 hours 30 minutes
= 4.5 hours
Average speed = Total distance travelled / Total time taken
= 585 km / 4.5 hours
= 130 kilometer/hour
Difference, in km/h, between the average speed of their trains = Lei's train - Ardi's train
= 130 kilometer/hour - 120 kilometer/hour
= 10 kilometer/hour
PLEASE HELP!!!
Which of the following trigonometric expressions is equivalent to the x-
coordinate of the terminal point
Answer:
im pretty sure its (D)
Step-by-step explanation:
Lorraine computed a confidence interval for µ based on a sample of size 41. Since she did not know σ, she used s in her calculations. Lorraine used the normal distribution for the confidence interval instead of a Student's t distribution. Will her interval be longer or shorter than one obtained by using an appropriate Student's t distribution? Explain.
Answer:
Shorter
Step-by-step explanation:
When given the population standard deviation, σ, the normal distribution should be used. However, if the sample standard deviation is being used, the t distribution should be used. The implication of using a normal distribution in Lorraine's case when using the sample standard deviation which requires the use of the T - distribution is that, the interval beacjbea smaller as the critical value obtained is smaller than the T critical value with degree of freedom, n - 1 ; 41 - 1 = 40
At α = 0.05 ;
Tcritical, df = 40 = 2.02
Zcritical = 1.96
the perpendicular distance of p (3,4) from the y - a x is _____
Answer:
a
Step-by-step explanation:
The perpendicular distance from the y- axis is the value of the x- coordinate, so
perpendicular distance is 3 units
What is the value of d?
A.100 B.84 C.50 D.80
Answer:
A. 100
Step-by-step explanation:
84
Step-by-step explanation:
c + 100 =180
c=180-100
c=80
100+96+d+c=360
100+96+d+80=360
276+d=360
d=360-276
d=84
if f(x)=2x/x-5 find f^-1(x)
Answer:
[tex]f^{-1}[/tex] (x) = [tex]\frac{5x}{x-2}[/tex]
Step-by-step explanation:
let y = f(x) and rearrange making x the subject
y = [tex]\frac{2x}{x-5}[/tex] ( multiply both sides by x - 5 )
y(x - 5) = 2x ← distribute left side
xy - 5y = 2x ( subtract 2x from both sides )
xy - 2x - 5y = 0 ( add 5y to both sides )
xy - 2x = 5y ← factor out x from each term on the left side )
x(y - 2) - 5y ← divide both sides by y - 2
x = [tex]\frac{5y}{y-2}[/tex]
Change y back into terms of x with x = [tex]f^{-1}[/tex] (x) , then
[tex]f^{-1}[/tex] (x) = [tex]\frac{5x}{x-2}[/tex]
Look into the image. I hope it helps❤
#CarryOnLearningFind the answer to each trigonometric function below.
Answer:
Sin A = [tex]\frac{opposite}{hypotenuse} =\frac{32}{40} =\frac{4(8)}{5(8)} =\frac{4}{5}[/tex]Cos C = [tex]\frac{adjacent}{hypotenuse} =\frac{16}{34}=\frac{2(8)}{2(17)} =\frac{8}{17}[/tex]Tan A = [tex]\frac{opposite}{adjacent} =\frac{21}{20}[/tex]PLEASE HELP! Use the graph to solve the system of equations.
A. (-5,0)
B. (0,5)
C. (0,0)
D. (2,3)
Answer:
D
Step-by-step explanation:
Look for the intersection point of the two graphs
Another way:
You can just substitute each pair in both equations and u will find that d is the correct answer
please someone explain this
Answer: 68
Step-by-step explanation: Complementary angles are angles that add up to 90. So, you need to do 90-22=68.
Joe drinks some milk every day. The graph shows the proportional
relationship of how many liters of milk Joe drinks to number of days.
Find the amount of milk he drinks in 7 days.
====================================
Explanation:
Draw a vertical line up from x = 7 until you reach the diagonal red line. Mark point P at this location. Then from point P, move horizontally until you reach the y axis. You should get to y = 14.
See the diagram below.
The equation of this red line is y = 2x. Whatever the input x is, we double it to get y. So if x = 7, then y = 2x = 2*7 = 14
This means that Joe drinks 14 liters of milk in 7 days. Or you could say his rate is 14 liters per week.
Answer:
The correct answer is 14 liters
Step-by-step explanation:
When you look at the graph you can count the grid squares. In one day Joe drinks 2 liters of milk. So 7 times 2 is 14. That is your answer
Let me know if I did anything wrong. :)
Find P(5) given P(x) = 4 - 1
Answer:6
Step-by-step explanation:
sorry if im wrong
SOMEONE PLEASE HELPPPPPPPPPP
Answer:
the formula for the volume of a square pyramid is V=a^2*h/3
so if we just put in the data
12^2*10/3
144*10/3
480
so the answer is B
Hope This Helps!!!
what are all the factors 24? please help lol
Answer:
factors are 1,2,3,4,6,8,12,24
someone help me with my algebra homework please
Answer:
15
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
5a - 10b = 45
b = 3
Step 2: Solve for a
Substitute in b [Equation]: 5a - 10(3) = 45Multiply: 5a - 30 = 45[Addition Property of Equality] Add 30 on both sides: 5a = 75[Division Property of Equality] Divide 5 on both sides: a = 15Answer:
a=3
Step-by-step explanation:
5a-10b=45
when b=3
5a-10×3=45
5a-30=45
collect like terms
5a=45-30
5a=15
a=3
The Law of Sines: Mastery Test ? In triangle ABC, how long is side a if A = 24°, C = 55°, and c = 3? O 1.49 O 1.31 O 6.04 O 0.1
Answer:
Step-by-step explanation:
Using the Law of Sines, our proportion would be
[tex]\frac{sin24}{a}= \frac{sin55}{3}[/tex] and cross multiply to get
3sin24 = asin55 and solve for a:
[tex]a=\frac{3sin24}{sin55}[/tex] so
a = 1.49, the first choice.
In a geometric sequence, the term a(n+1) can be smaller than the term a(n-)
Answer:
the answer is true
Step-by-step explanation:
the ratio is less than 1
What is the domain of the function on the graph?
•all real numbers
•all real numbers greater than or equal to -2
•all real numbers greater than or equal to -5
•all real numbers greater than or equal to 0
Answer:
all real numbers
Step-by-step explanation:
got it right
Answer:
A
Step-by-step explanation:
it is all real numbers
brainiest please
El solar de Maria tiene forma rectangular los lados miden 36 cm y 40 cm ¿Cuántos metros cuadrados tiene el terreno? ¿Cuál es el perímetro del terreno?
Respuesta:
Área del rectángulo = 0.144m²
Perímetro del rectángulo = 1,52 m²
Explicación paso a paso:
Dado que el área del rectángulo = Largo * Ancho
Convertir cm a m
Los 36cm = los 0.36m
Los 40cm = los 0.4m
Sustituir;
Área del rectángulo = 0.36 * 0.4
Área del rectángulo = 0.144m²
Perímetro del rectángulo = 2 (L + W)
Perímetro del rectángulo = 2 (0.36 + 0.4)
Perímetro del rectángulo = 2 (0,76)
Perímetro del rectángulo = 1,52 m²
It has been reported that the average credit card debt for college seniors is $3262. The student senate at a large university feels that their seniors have a debt much less than this, so it conducts a study of 50 randomly selected seniors and finds that the average debt is $2995, and the population standard deviation is $1100. At α = 0.05, is the student senate correct? a) State the hypotheses and identify the claim with the correct hypothesis
Answer:
Following are the solution to the given point:
Step-by-step explanation:
The formulated null hypothesis would be that the reported average do not differ significantly
[tex]H_o : \mu = \$3262\\\\H_a : \mu < \$3262 \ \text{(One tailed test)}[/tex]
What ordered pairs are the solutions of the system of equations shown in the graph below?
Answer:
(1,-3) and (4,-6)
Step-by-step explanation:
The solutions are where the linear line intersects the graphed parabola.
The ages of Raju and Ravi arw the ratio of their ages will be 4:5 . Find their present ages.
Answer:
Step-by-step explanation:
The ages of Raju and Ravi are in the ratio 3:4 .Four years from now the ratio of their ages will be 4:5 . Find their present ages.
Ratio of ages at present = 3:4
Age of Raju = 3x
Age of Ravi = 4x
Age after four years:
Raju's age = 3x + 4
Ravi's age = 4x + 4
Ratio of ages after four year = 4 : 5
3x +4 : 4x + 4 = 4 : 5
(4x + 4)*4 = (3x + 4)*5
16x + 16 = 15x + 20
Subtract 16 from both sides
16x = 15x + 20 - 16
16x = 15x + 4
Subtract 15x from both sides
16x - 15x = 4
x = 4
Age of Raju = 3x = 3*4 = 12 years
Age of Ravi = 4x = 4*4 = 16 years
Please help me with 1-6 (means) ASAPPPPP
I will give brainiest
Answer:
Geometric mean of [8,18] = 12Geometric mean of [3,7] = 4.58Geometric mean of [5,8] = 6.32Geometric mean of [8,4] = 5.65Geometric mean of [6,3] = 4.24Geometric mean of [2,8] = 4Step-by-step explanation:
Given:
Geometric mean of two digit = √ab
Answer 1;
Geometric mean of [8,18] = √(8)(18)
Geometric mean of [8,18] = √144
Geometric mean of [8,18] = 12
Answer 2;
Geometric mean of [3,7] = √(3)(7)
Geometric mean of [3,7] = √21
Geometric mean of [3,7] = 4.58
Answer 3;
Geometric mean of [5,8] = √(5)(8)
Geometric mean of [5,8] = √40
Geometric mean of [5,8] = 6.32
Answer 4;
Geometric mean of [8,4] = √(8)(4)
Geometric mean of [8,4] = √32
Geometric mean of [8,4] = 5.65
Answer 5;
Geometric mean of [6,3] = √(3)(6)
Geometric mean of [6,3] = √18
Geometric mean of [6,3] = 4.24
Answer 6;
Geometric mean of [2,8] = √(2)(8)
Geometric mean of [2,8] = √16
Geometric mean of [2,8] = 4
Please help me I keep on getting the third box wrong
Answer:
[tex](2 {a}^{2} + 1)(1 {a}^{2} + 9)[/tex]
Step-by-step explanation:
[tex]2 {a}^{4} + 19 {a}^{2} + 9 \\ 2 {a}^{4} + {a}^{2} + 18{a}^{2} + 9 \\ {a}^{2} (2 {a}^{2} + 1) + 9(2 {a}^{2} + 1) \\ (2 {a}^{2} + 1)( {a}^{2} + 9) \\ [/tex]
A certain jet can reach an altitude of 8000 ft while flying 16000 ft through the air. what is the angle of the elevation that the plane is flying? Round to the nearest degree.
Answer:
27 degrees
Step-by-step explanation:
First, we can draw this out. Since the altitude is 8000, we can make that the height, and it goes 16000 feet through the air, that can be the length. I have drawn this out, as shown in the image. Note that when drawing, because the airplane is going up and forward, that path should represent the hypotenuse. The angle of elevation is the angle connecting the length and the path, as shown by the angle x in the picture.
We know than tan(x) = opposite/adjacent, so tan(x) here = 8000/16000 = 1/2. Then, arctan(1/2) =x = 27 degrees
convert 0.25151 to a fraction
Answer:
25151/100000
Step-by-step explanation: