What are the solutions of the quadratic equation 49x2 = 9? x = StartFraction 1 Over 9 EndFraction and x = StartFraction negative 1 Over 9 EndFraction x = StartFraction 3 Over 7 EndFraction and x = Start Fraction negative 3 Over 7 EndFraction x = StartFraction 3 Over 4 EndFraction and x = StartFraction negative 3 Over 4 EndFraction x = StartFraction Over 49 EndFraction and x = StartFraction negative 9 Over 49 EndFraction

Answer:

Angles A and E are congruent.

Step-by-step explanation:

Angles A and E are congruent because they are alternate interior angles.

Angle A and E are congruent angles. Option A is correct.

In given figure, Line D E and Line A B are parallel.

Which angles are congruent to be determined?

In congruent geometry, the shapes that are so identical. can be superimposed to themselves.

Parallel lines are defined as the lines in which every point is equidistant from the corresponding point on the other line and the parallel line met it infinity.

By property of the parallel line, when a line intersect numbers of parallel line the alternate opposite angles are equal.
By property and clear observatin Angle, A is congruent with Angle E. and Angle D is congruent with Angle B, Hence Option A is correct and all the option can be omitted.

Thus, Angle A and E are congruent angles. Option A is correct.

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Step-by-step explanation:

Consecutive even integers are like 2, 4, 6, etc. So the equation would be:

x + x+2 + x+4 + x+6 = 292

Combine the like terms, x and the number values, to get:

4x + 12 = 292

Isolate x by subtracting 12 on both sides:

4x = 280

Divide by 4:

x = 70

Then plug in the value for x:

70, 72, 74, 76

The four consecutive even integers that sum up to 292 are 70, 72, 74, and 76.

To find 4 consecutive even numbers that sum to 292, let’s first understand what consecutive even numbers are. Consecutive even numbers are even numbers that follow each other in order. For instance, 2, 4, 6, 8 are four consecutive even numbers because each number is 2 more than the previous number.

Let's label the first of our 4 consecutive even numbers as 'x'. Each subsequent number is an increase of 2, so we can label them as 'x+2', 'x+4', and 'x+6'.

According to the question, the sum of these four integers is 292, so we form an equation: x + (x+2) + (x+4) + (x+6) = 292. Combining like terms, we get 4x + 12 = 292. Subtracting 12 from both sides of the equation: 4x = 280. Dividing both sides by 4 to solve for x, we find that x = 70.

So, using our labels from earlier, our four integers are 70, 72, 74, and 76.

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Answer:

Confidence levels and P-values from the t procedures are quite accurate even if the population distribution is not exactly Normal

Step-by-step explanation:

Confidence levels and P-values from the t procedures are quite accurate even if the population distribution is not exactly Normal

there is a general rule that depicts that T is okay to use when n >30. also when the sampling method for each sample is simple random sampling and samples are independent.

Answer:

The randomization distribution is created under the assumption that H₀: p = 0.1

The randomization distribution will also be centred at 0.1

Step-by-step explanation:

If the distribution was truly random, 1 out of 10 students will choose math as his/her favorite subject.

This means that the randomization will have the null hypothesis saying that the proportion of students who will choose maths as their favourite subject = 0.1

Mathematically, it'll be written as

The null hypothesis is given as

H₀: p = 0.1

And the randomization distribution will be centred at 0.1 too.

The alternative hypothesis will now prove the theory they're looking to see in the question that

Hₐ: p < 0.1

Hope this Helps!!!

Answer:

1/2

Thats about it

Answer:

A. There is enough evidence that p < 0.05 that the mean distance between ball one and two as measured by his computed tomography machine is greater than 16.02mm.

Step-by-step explanation:

n= 5

x bar= 16.02

Standard Error= 0.02236

NB:

The null hypothesis is referred to as a characteristic arithmetic theory that gives a statement that suggests that no statistical relationship and significance exists in a set of given observed variables between two sets of observed data and also, measured phenomena. The hypotheses play a crucial role in testing the significance of differences in experiments and between observations. H o represents the null hypothesis of no difference.

The alternative hypothesis is generally represented as H1. It makes a statement that suggests a potential result or an outcome that a researcher may expect.

Standard error measures how far the sample mean of the data is most likely to be from the true population mean.

We want to test the null and alternative hypothesis

H o : μ = 15.96 vs H1 : μ > 15.96

1. Test statistics

Z= xbar - μ / Standard error

Z= 16.02 - 15.96 / 0.002236

Z= 2.6834

2. P value= 0.0036

3. Yes, there is enough evidence that p < 0.05 that the mean distance between ball one and two as measured by his computed tomography machine is greater than 16.02mm.

Therefore, option A is the correct answer.

Answer:

123

Step-by-step explanation:

The complete question is Assume that X/Y=M/N . Which of the following statements are true? (Assume that X, Y, M, N, and F are nonzero real numbers, and assume that all expressions have nonzero denominators.) Create an answer using the numbers associated with the true statements. For example, if only 1, 2, and 5 are true, then the answer is 125; if only 3 and 5 are true, then the answer is 35, etc

The statements are given in 1st attachment and answer choices are given in 2nd attachment

Let's start by verifying statements 3 and 4 as these are easy to verify

To verify statement 3,

(X+Y)/Y= (M+N)/N

X/Y + 1= M/N + 1

since X/Y=M/N

X/Y + 1=  X/Y +1

So statement 3 is true

To verify statement 4,

(X+F)/Y= (M+F)/N

X/Y + F/Y = M/N + F/N

Statement 4 is false

Look at the answer choices, statement 3 is mentioned in option c,d and e. Statement 4 is mentioned in c and d. Since statement 4 is incorrect our answer is option e

Final answer:

Option B: the number that represents the middle value in the set of numbers

Explanation:

The median is a statistical measure that represents the middle value in a set of numbers.

To find the median, first, the numbers must be arranged in ascending order. If the number of values (n) in the dataset is odd, the median is the middle value directly.

If n is even, the median is the average of the two middle values. It effectively separates the dataset into two halves, where half of the values are equal to or less than the median, and the other half are equal to or greater than the median value.

For example, in the data set {3, 4, 5, 9, 11}, the median is 5, as it is the middle value of the ordered set.

In another set with an even number of values, for instance, {3, 4, 7, 10}, the median would be the average of 4 and 7, which is 5.5.

This concept is important especially when dealing with outliers, or extreme values, as the median is not affected by them like the mean (average) would be.

Answer:

p(x = 3, λ = 5) = 0.14044

Step-by-step explanation:

Given

λ = 5 (the average number of tracks per square centimeter)

ε = 2.718 (constant value)

x = 3 (the variable that denotes the number of successes that we want to occur)

p(x,λ) = probability of x successes, when the average number of occurrences of them is λ

We can use the equation

p(x,λ) = λˣ*ε∧(-λ)/x!

⇒ p(x = 3, λ = 5) = (5)³*(2.718)⁻⁵/3!

⇒ p(x = 3, λ = 5) = 0.14044

Answer:

0.0108

Step-by-step explanation:

Let X denote the number of uranium fission tracks occurring on the average 5 per square centimetre.We need to find the probability that a 2cm² sample of this zircon will reveal at most three tracks. X follows Poisson distribution, λ = 5 and s = 2.

k = λs = 5×2 = 10

Since we need to reveal at most three tracks the required probability is:

P (X≤3) = P (X =0) + P (X =1) + P (X =2) + P (X =3)

P (X≤3)  = (((e^​-10) × (10)⁰)/0!) +  (((e^​-10) × (10)¹)/1! +  (((e^​-10) × (10)²)/2! + (((e^​-10) × (10)3)/3!

P (X≤3)  = 0.0004 + 0.0005 +0.0023 +0.0076

P (X≤3)  = 0.0108

Therefore, the probability that a 2cm² sample of this zircon will reveal at most three tracks is 0.0108

C.10

Explanation

From table critical value of U when n1 is 7 and n2 is 8 and symbol alpha is 0.05 then Ucrit=10

The Mann-Whitney U test was used to compare study times between Psychology and English majors. The U value computed was 0.5, which is less than the critical value of 46. Therefore, the correct answer is A) 07.

To determine if there is a difference in the studying time between Psychology and English majors, the student is using the Mann-Whitney U test. The Mann-Whitney U test is a non-parametric test used to compare differences between two independent groups when the dependent variable is either ordinal or continuous, but not normally distributed.

Here are the given study times:

First, we need to rank all the study times from both groups combined, from lowest to highest, and then sum the ranks for each group.

Ranks:
Psychology Majors: 16 (10.5), 12 (7), 13 (8), 10 (4), 9 (3), 10 (4), 8 (2)
English Majors: 10 (4), 25 (16), 15 (9), 17 (13), 23 (15), 14 (8), 19 (14), 18 (12)

Sum of ranks:
Psychology Majors: 49.5
English Majors: 91.5

Using these ranks and sums, we calculate the U values:

The Mann-Whitney U value is the smaller of U1 and U2, so U = 0.5. Given that Ucrit = 46 at α = 0.05, 2-tailed, we compare our U value to Ucrit.

Because 0.5 < 46, we reject the null hypothesis.

The correct answer choice is A) 07.

Answer:

its 3mm i promise its right pls make me brainliest

Step-by-step explanation:

Answer:

the answer is 3mm

Step-by-step explanation:

got it right on edge trust me the other guy is right to.

Answer:

96.24% probability that a SRS of 25 students will spend an average of between 600 and 700 dollars

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

[tex]\mu = 650, \sigma = 120, n = 25, s = \frac{120}{\sqrt{25}} = 24[/tex]

What is the probability that a SRS of 25 students will spend an average of between 600 and 700 dollars

This is the pvalue of Z when X = 700 subtracted by the pvalue of Z when X = 600. So

X = 700

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{700 - 650}{24}[/tex]

[tex]Z = 2.08[/tex]

[tex]Z = 2.08[/tex] has a pvalue of 0.9812

X = 600

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{600 - 650}{24}[/tex]

[tex]Z = -2.08[/tex]

[tex]Z = -2.08[/tex] has a pvalue of 0.0188

0.9812 - 0.0188 = 0.9624

96.24% probability that a SRS of 25 students will spend an average of between 600 and 700 dollars

Answer:

-3

Step-by-step explanation:

3 - |-4| - |2|

= 3 - 4 - |2|

= -1 - |2|

= 1 - 2

= -3

(Hope this helps)

Answer:

2 a) In Randomized Block design there are two variables one is a blocking variable the other one will be the treatment variable. Here type of shoes is the treatment variable and the type of runner is the blocking variable. Blocking is the arrangement of subjects similar in certain characteristics in to a group. Here professional runners are different from recreational runners . Blocking is done to reduce variability within groups so that variability within blocks is less than the variability between blocks. Then, subjects within each block are randomly assigned one of the shoes.

b) Randomization is the process of assigning participants a specific treatment  so that each participant has an equal chance of being assigned a shoe A or B. Randomization is done using random number generation and assignment is made according to the random numbers The main purpose of randomization is to eliminate biases. If the person in a group are allowed to choose the shoes they may choose their preferred one based on their past experience of using it or one variety will be preferred by most of the subjects in the group spoiling the entire purpose of the study. for e.g a group of professionals coming from a particular region prefers type A . If randomization is employed in such a situation almost half of the professionals coming from a particular region gets type A and the other half may get type B thus eliminating the personal biases in choice. This way we can eliminate any possible biases that may arise in the experiment. So randomization and blocking are important for a randomized block design in order to minimize bias in the responses.

Step-by-step explanation:

Answer:

500

Step-by-step explanation:

Lets make the unknown number the letter a

0.9% can also be shown as 0.9/100

so 0.9 of a = 4.5

x(0.9/100) = 4.5

multiply 0.9 by x

(0.9×a)/100 = 4.5

multiply both sides by 100

0.9×a = 450

divide both sides by 0.9

a = 500

there you have it

To determine the number that 4.5 is 0.9% of, we convert 0.9% to a decimal by dividing by 100 and solve the resulting equation. The answer is that 4.5 is 0.9% of 500.

To find the number that 4.5 represents 0.9% of, we should first convert the percent to a decimal. According to B.4, a percent is converted to a decimal by dividing the percent value by 100. In our case, 0.9% becomes 0.009.

Once we have the decimal equivalent of the percent, we can set up the equation where 4.5 is 0.9% (0.009 in decimal form) of some number x:

4.5 = 0.009x

To solve for x, divide both sides of the equation by 0.009:

x = 4.5 / 0.009

x = 500

Therefore, 4.5 is 0.9% of 500.

Answer:

a. discrete random variable

Step-by-step explanation:

A discrete random variable is one which may take on only a countable number of distinct values such as 0, 1, 2, 3, 4, etc. Discrete random variables are usually countable.

From the question:

The experiment consist of making 80 telephone calls in order to sell a particular insurance policy. 80 here is the random variable; 80 is countable anf finite.

So, 80 is a discrete random variable

In the experiment involving making 80 telephone calls to sell an insurance policy, the random variable is the outcome of each call, which can be represented as a countable number. Therefore, it's a discrete random variable, where possibilities could be represented by integers, unlike a continuous random variable which can take on infinite possible outcomes.

In the context of the question, where an experiment involves making 80 telephone calls to sell a particular insurance policy, the random variable is defined as the outcome of each call — specifically, whether each call results in a sale or not. This outcome is countable and finite, so it is a discrete random variable.

By definition, a discrete random variable is a variable that can only take on a finite or countable number of values. Some examples of discrete random variables are the number of books on a shelf or the number of students in a class. Here, in the case of the telephone calls, the possibilities could be represented by integers (e.g., 0 indicating no sale and 1 indicating a sale).

On the other hand, a continuous random variable, such as the weight of a book or the amount of time a telephone call lasts, can take on any value within a specified range. These variables are associated with measurements and can have infinite possible outcomes within a given interval.

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Given:

ΔABC undergoes a dilation by a scale factor and comes as ΔA'B'C'.

To show that both the triangles are similar.

Formula

If two triangles have three pairs of sides in the same ratio, then the triangles are similar.

[tex]Hypotenuse^2 = Base^2+Height^2[/tex]

Now,

In ΔABC,

AB = 18 unit

BC = 10 unit

So, [tex]AC^2 = AB^2+BC^2[/tex]

or, [tex]AC^2 = 18^2+10^2[/tex]

or, [tex]AC = \sqrt{424}[/tex]

Again,

In ΔA'B'C'

A'B' = 9 unit

B'C' = 5 unit

So, [tex]A'C' ^2 = A'B'^2+B'C'^2[/tex]

or, [tex]A'C'^2 = 9^2+5^2[/tex]

or, [tex]A'C' = \sqrt{106}[/tex]

Now,

[tex]\frac{AB}{A'B'} = \frac{18}{9} = 2[/tex]

[tex]\frac{BC}{B'C'} = \frac{10}{5} = 2[/tex]

[tex]\frac{AC}{A'C'} = \frac{\sqrt{424} }{\sqrt{106} } = 2[/tex]

Hence,

All the ratios are equal.

Therefore, we can conclude that,

ΔABC and ΔA'B'C' are similar.

Answer:

The statistic is z=-0.674.

The null hypothesis failed to be rejected.

Step-by-step explanation:

To make conclusions about the effectiveness of the new method, they should perform an hypothesis test on the proportion of failed cancer detection.

The actual method has a proportion of failed cancer detection of p=0.15. If the new method is better, it should have enough evidence that its actual proportion is below 0.15. This claim, that the new method proportion is below 0.15, will be stated in the alternative hypothesis.

The null and alternative hypothesis are:

[tex]H_0: \pi=0.15\\\\H_a:\pi<0.15[/tex]

The sample size is n=70.

The sample proportion is p=8/70=0.114.

The standard error is calculated as:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.15*0.85}{70}}=\sqrt{0.0018}=0.043[/tex]

Then, the z-statistic for this sample is:

[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.114-0.15+0.5/70}{0.043}=\dfrac{-0.029}{0.043} =-0.674[/tex]

The P-value for this statistic is:

[tex]P-value=P(z<-0.674)=0.25[/tex]

At a significance level of 0.1, the P-value is bigger, so the effect is not significant. The null hypothesis failed to be rejected.

Answer:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

[tex]z=\frac{0.114 -0.15}{\sqrt{\frac{0.15(1-0.15)}{70}}}=-0.844[/tex]  

Step-by-step explanation:

Data given and notation

n=70 represent the random sample taken

X=8 represent the number of the new method failed to detect cancer

[tex]\hat p=\frac{8}{70}=0.114[/tex] estimated proportion of number of the new method failed to detect cancer

[tex]p_o=0.15[/tex] is the value that we want to test

[tex]\alpha[/tex] represent the significance level

z would represent the statistic (variable of interest)

[tex]p_v[/tex] represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the new method is able to detect cancer more accurately than the currently method (that means a lower rate of the proportion of interest) .:  

Null hypothesis:[tex]p \geq 0.15[/tex]  

Alternative hypothesis:[tex]p < 0.15[/tex]  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.114 -0.15}{\sqrt{\frac{0.15(1-0.15)}{70}}}=-0.844[/tex]  

Answer:

attached

Step-by-step explanation:

attached

Answer: 176 degrees and 4 degrees.

Step-by-step explanation: To find the measure of the angles, all you have to do is create an equation. Let's call the supplementary angle x and the other angle 44x, because the other angle is 44*the supplementary angle. Now, we structure the equation 44x + x = 180. The reason we say the sum of the angles is 180 is because any angle plus its supplementary angle equals 180 degrees. From there it's just algebra:

44x + x = 180

45x = 180

x = 180/45

x = 4

We can check our work by substituting x for 4 in the equation:

44*4 + 4 = 180

174 + 4 = 180

180 = 180

Thus, the first angle is 176 degrees and the second is 4 degrees.

The diameter of the traffic cone= 0.4604

Step-by-step explanation:

The volume of the cone= 150 cubic inches.

The height of the cone= 18 inches.

The volume of the cone= (1/3) x pi x R² x H

                                150 = (1/3) x (22/7) x R² x 18

                                  R² = 3 x 7/ 22 x 18

                                  R² = 0.0530

                                   R = 0.2302

                   Diameter, D= R x 2

                                    D= 0.2302 x 2

                   Diameter, D= 0.4604

Answer:

The central angle of the arc is 288 degrees

Step-by-step explanation:

The correct question is

A circle has a circumference of 8. It has an arc of length 32/5 . What is the central angle of the arc,in the degrees?

we know that

The circumference of the circle subtend a central angle of 360 degrees

so

uing a proportion

Find out the central angle for an arc of length 32/5

[tex]\frac{8}{360^o}=\frac{(32/5)}{x}\\\\x=360(32/5)/8\\\\x=288^o[/tex]

Answer:

288

Step-by-step explanation:

Answer:

y = -1.5x + 11

Step-by-step explanation:

Because the line is parallel, the equation will have the same slope.  To find the slope, convert the given equation to y=mx+b form.  The equation you get should be y = -1.5x + 3.  The slope will be -1.5.

Now using the y=mx+b form, plug in the points given and the slope we found and solve for b.  

5 = -1.5(4) + b

b = 11

Now, with the slope and b, you should get the equation y = -1.5x + 11.

Answer:

1.a. H₀: μ₁ - μ₂ ≤ 0

2.b. H₁: μ₁ - μ₂ > 0

Step-by-step explanation:

Hello!

The objective is to compare the average training time for two groups of airport security personnel.

Group 1: Security personnel that works for the federal government

n= 12

X[bar]= 72 hs

S= 8hs

Group 2: Security personnel from private companies

n= 16

X[bar]= 65.4 hs

S= 12.3 hs

The goal of the analysis is to test if the average training time for government-employed security personnel is higher than those employed by private security companies, symbolically: μ₁ > μ₂

The null and alternative hypotheses are complementary and exhaustive.

The null hypothesis always represents the "no change situation" and therefore always carries the = symbol. Generally, the researcher's claim is stated in the alternative hypothesis.

With all this in consideration, the hypotheses for this experiment are:

H₀: μ₁ ≤ μ₂

H₁: μ₁ > μ₂

I hope this helps!

Answer:

11.55% probability that the purchase was made with a mobile device and was from Amazon.

Step-by-step explanation:

We have these following probabilities:

21% probability that a Cyber Monday shopper used their mobile device to make a purchase.

55% probability that a purchase made with a mobile device is from Amazon.

What is the probability that the purchase was made with a mobile device and was from Amazon."

55% of 21%

So

P = 0.21*0.55 = 0.1155

11.55% probability that the purchase was made with a mobile device and was from Amazon.

Answer:

first  6 x 4 = 24

Step-by-step explanation:

second, 120 divided by by the hours which is 24.

so 120 divided by 24 = 5

5 = answer

Given Information:

Probability of success = p = 0.06

Number of trials = n = 20

Required Information:

Probability of 1 or more donors of "O" blood group = ?

Answer:

P( x ≥ 1 ) = 0.710

Step-by-step explanation:

We are given the probability that a donor has type "O" blood group.

We want to find out the probability of having 1 or more donors who has type "O" blood group out of 20 donors.

P( x ≥ 1 ) = 1 - P( x = 0)

So we will first find the probability that none of the donors has type "O" blood group then we will subtract that from 1 to get the probability of having 1 or more donors with "O" blood group.

P( x = 0) = (p⁰)(1 - p)²⁰

P( x = 0) = (0.06⁰)(1 - 0.06)²⁰

P( x = 0) = (1)(0.94)²⁰

P( x = 0) = 0.290

So the probability of having 1 or more donors with "O" blood group is

P( x ≥ 1 ) = 1 - P( x = 0)

P( x ≥ 1 ) = 1 - 0.290

P( x ≥ 1 ) = 0.710

P( x ≥ 1 ) = 71%

Therefore, the correct answer is D. 0.710

Final answer:

The probability that 1 or more donors have type O blood is approximately 0.370.

Explanation:

The probability that 1 or more donors have type O blood can be found using the complement rule. The complement of the event that 0 donors have type O blood is the event that 1 or more donors have type O blood.

The probability that a donor has type O blood is 0.06. The probability that a donor does not have type O blood is 1 - 0.06 = 0.94. Let's calculate the complement probability:

P(1 or more donors have type O blood) = 1 - P(0 donors have type O blood)

= 1 - (0.94)^{20} (since the donors are independent)

Using a calculator, we get P(1 or more donors have type O blood) ≈ 0.370

Answer: The test statistic is -3.322.

Step-by-step explanation:

Since we have given that

n = 431

[tex]\hat{p}=0.42[/tex]

Hypothesis would be :

[tex]H_0:p=0.5\\\\H_1:p\neq 0.5[/tex]

So, the test statistic would be

[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\z=\dfrac{0.42-0.5}{\sqrt{\dfrac{0.5\times 0.5}{431}}}\\\\z=\dfrac{-0.08}{0.02408}\\\\z=-3.322[/tex]

Hence, the test statistic is -3.322.